Well, no doubt seeking help from a professional __math problem solver__** **is the best way to solve your quadratic equations right away. However, trying your own hands on the same will also help you upgrade your problem-solving skills. So, proceed with your reading and focus on the various ways to solve Quadratic equations with complex solutions. But before that, let’s learn about the various quadratic equation types.

**Standard Form: **

ax2 + bx + c = 0

Here,

a, b and c are leading coefficients besides being non-zero real numbers.

- ‘a’ is the coefficient of x2
- ‘b’ is the coefficient of x
- ‘c’ is the constant

**Factored Form:**

In a Factored form of a Quadratic equation, the sum gets written as ax2 + bx + c = 0, as a product of its linear factors as (x – k)(x – h). Where ‘h’ and ‘k’ are basically the roots of the quadratic equation ax2 + bx + c = 0. Also, a quadratic equation can be factored in by creating a split between the middle term with the help of a quadratic formula and completing squares.

**Vertex Form**:

You can find coordinates at a certain point with a Vertex Formula in a quadratic equation. Also, there will be a parabola crossing the axis of symmetry. The formula goes as y=a(x−h)2+k. Here, y is the y-coordinate, x is the x-coordinate, and ‘a’ is the constant, telling you whether the parabola is facing up (+a) or down (−a).

**Pro Tip**: You can also seek help and ask to do my homework experts are available online and get away with the equations in real-time.

Terms you must know in a Quadratic Equation:

**Coefficient: **The number that can multiply the variable using a specific amount. For example, the 2 in 2x.

**‘Completing the square’: **You must divide all the terms using the coefficient and add/subtract the constant terms.

**Constant: **It is a fixed value within an equation.

**Degree: **The largest exponent within an equation. The squared x denotes a quadratic equation, whereas an x with a third degree indicates a cubic equation.

**Discriminant: **It denotes if there is a real number solution within the equation.

**Factoring: **Here, you need to look at the multi pliable factors within the equation.

**Parabola: **A “plane curve” also represents the “graphed version” of a quadratic equation.

**Quadratic Equation: **Here, the highest exponent of a variable is squared.

**Quadratic Function: **The equation is expressed as f(x) = a(x-h)2 van also be used to graph a parabola.

**Real Number: **Numbers that get positive results when multiplied by themselves.

**Variable: **Letter within a Mathematical expression that represents an unknown value.

**Vertex: **It can be a minimum or a maximum value within a quadratic function (graphed). The same is represented within a point where the parabola changes direction.

**Quadratic formula**: The formula used in solving a quadratic equation.

Steps in solving a quadratic equation:

**Factor equations**:

**Create a combination of all the like terms and move them towards one side**: The very first step is moving all the terms towards one side, keeping the x2 term positive. To create a combination of terms, keep adding or subtracting all the x2 and the x terms. Until nothing is left on the other side except 0.

**Factor the expression**: Use the factor of the x2 term to factor the equation. You can also take help from an **online math problem solver **accordingly.

**Set each set of parenthesis = zero as separate equations**: You will get to find two values of x, making the entire equation similar to zero.

Solve each “zeroed” equation independently: Now it’s time to solve the values independently.

**Proceeding forward:**

- Checking x equal to -1/3 in (3x + 1)(x – 4) = 0
- Checking x equal to 4 in (3x + 1)(x – 4) = 0

** **

**Using the Quadratic Formula**

**Combine all the like terms and move them to one side: **Keep the squared form of x positive and move the rest of the terms to one side of the “=” sign.

**Write down the quadratic formula: **It’s time to write down the quadratic formula. You can use a **written math problem solver **in this case.

**Identify the values of a, b, and c in the quadratic equation: **Take the variable ‘a’ as the coefficient of the squared x term and ‘b’ as the coefficient of the regular x term. Here ‘c’ is the constant.

**Substitute the values of a, b, and c into the equation: **Now, substitute the values of the three terms a,b and c and plug the within the equation.

**Do the math: **Once done with the plugged-in part, it’s time to do the Math.

**Simplify the square root: **If the number under the radical symbol happens to be a perfect square, you are probably going to get a whole number.

**Proceed forward: **

Solving for the positive and negative answers

Solving for the positive and negative answers

**Simplify: **Divide the numbers by the largest available number to simplify each answer.

**Complete the square: **

**Move everything in the equation to one side: **Make sure that the squared ‘x’ and ‘a’ terms are positive in this case.

**Move c to the other side: **The ‘c’ will be on the right side of the equation.

**Use the squared x or a specific term to divide both sides by the coefficient: **You can skip this if there is no other term in front of the squared x. ** **

** ****Divide b by two, come up with a square, and add the new results on both sides: **Here is how you do it:

**It’s time to simplify both sides: **Here, you will have to factor terms on your left.

Add the remaining terms on your right.

** **Adding up as:

**Detect square roots of both sides: **You can write the square root as

Therefore,

** ****Simplify the radical value and come up with solutions for x: **The final output is

** ****Final Thoughts**

You need thorough consistency and daily practice to come up with quick solutions to complex Quadratic equations. However, make sure to follow adequate steps and not skip any. Otherwise, it will lead to unnecessary hassles.

**Author Bio**: Mike Brian lives in New York, USA, and has recently joined the core team of Tophomeworkhelper.com. Here, he is responsible for helping subject matter experts with their editing and proofreading tasks. Mike is also experienced as a professional **Math problem solver **and has been serving the industry for some time now.