Quadratic Equations

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What is a Quadratic Equation? A quadratic equation is a single-variable equation in which the highest power on the variable is 2. The standard form is:
${ax}^{2}+bx+c=0$
where $a$, $b$, and $c$ are real numbers and $a\ne 0$ .

Solving Quadratic Equations There are three methods for solving a quadratic equations:
Factoring
Factoring is a process of changing the form of an equation from the standard form into the product of two factors:
$\left(ax+b\right)\left(cx+d\right)=0$
Once the equation is in this form, each factor is set equal to 0 and solved for x. This uses the Zero-Product Property that says if the product of two factors equals zero, then at least one of the factors must equal zero.
$\left(ax+b\right)=0$ OR $\left(cx+d\right)=0$
Completing the Square
Completing the square is a process of changing the form of an equation from the standard form so that both sides are perfect squares:
${\left(x+b\right)}^{2}={c}^{2}$
Once it’s in this form, the solutions can be found by taking the square root of both sides and solving for x.

Quadratic Formula
The quadratic formula is:
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
I prefer this form:
$x=\frac{-b±\sqrt{d}}{2a}$ where $d$ is the discriminant ${b}^{2}-4ac$

Solve a Quadratic Equation
 Enter values for: Choose your method(s): Solve it! $a$ $b$ $c$ Factoring Completing the Square Quadratic Formula ${x}^{2}+$ $x+$ $=0$

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