A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

### Notes

A quadratic equation is any function that has the form: ax

^{2} + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are called coefficients. Also, it should be mentioned that a cannot equal to 0 in the equation ax

^{2}+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is relatively basic. Solving a quadratic equation requires some more advanced mathematics. Fortunately, any quadratic equation can readily be solved using the

quadratic formula. The quadratic formula is written:

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Under extraordinary circumstances, the two roots may be equal, meaning there will only be one solution for x.

Quadratic equations are more than just mathematical chores we have to endure. Quadratic equations are needed to find answers to many real-world problems. For example, to calculate how an object will rise and fall due to Earth's gravity would require the use of s quadratic equation.

As mentioned above, in the equation ax

^{2}+bx+c=0, a cannot be zero. If a were 0, then ax

^{2} = 0x

^{2} = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

We hope you find this quadratic equation solver useful. We hope the explanations showing how you can solve the equation yourself are educational and helpful. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

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