A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.
A quadratic equation is an equation
+ bx + c = 0.
\ In this equation, x is a variable of unknown value. A, b, and c are constants. The constants a and b are called coefficients. Interestingly, a cannot be equal to 0 in the equation ax2
+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.
Solving a linear equation is rather straightforward. Solving a quadratic equation requires more work. Fortunately, any quadratic equation can reliably be solved using the quadratic formula
. This is the quadratic formula:
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, these two roots may have the same value, meaning there will only be one solution for x.
There are many uses for quadratic equations. Quadratic equations are needed to find answers in many real-world fields, including physics, biology and business.
As mentioned above, in the equation ax2
+bx+c=0, a cannot be zero. If a were 0, then ax2
= 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 encourage you to plug in different values for a, b, and c. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.
for a random example of a quadratic equation.