The Steps to Solve Quadratic Equations

By Allison Horky
Only terms with matching variables and exponents can be added.
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The quadratic equation is most often used to solve curves on a graph when an object is experiencing projectile motion. The sides of the curve intersect the x-axis twice and y-axis once. The two answers the equation yields are the x-axis intersectioning points. The equation uses coefficients, a number multipied by a variable, and is equal to zero. Once you plug in your known values for the coefficients, you can solve for x.

Set Up the Equation

Write the quadratic equation on a piece of paper. If you are solving for "x," the equation should read x = (-b ± √((b^2)-4ac)))/2a. The equation yields two answers for "x," corresponding to their location on the x-axis. The equation reads "x" equals the opposite of "b" plus or minus the square root of "b" squared minus 4 times "a" times "c" divided by 2 times "a." Also write the values you know about your curve; for example, if "a" equals 3, "b" equals 20 and "c" equals 10. Plug your known values into the quadratic equation. Using the example numbers given, you have x = (-5 ± √((20^2)-(4x3x10)))/(2x3).

Solve the Equation

Solve the equation according to the order of operations to obtain a value for "x." Solve the value that is squared first and the numbers that are multiplied by each other second. The example now reads x = (-5 ± √(400-120))/6. Solve the subraction before solving for the square root phrases in the equation. The example now reads x = (-5 ± 16.73)/6.

Reaching the Answer

Solve for "x" by adding or subtracting the numbers on the top of the equation and dividing it by the number on the bottom. The equation uses a ± sign, read plus or minus sign, because the equation needs to yield two values. The two values represent where the two sides of the curve intersect the x-axis on a graph. The answers to the example problem are x = -3.62 and x = 1.96.

Plot the Points

On a graph, the first value is to the left of the y-axis on the negative side of the x-axis; the second value is to the right of the y-axis, on the positive side. Having these values enables you to solve for other properties of the curve, such as area.