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Question
x^{2}=x+12
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
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x_{1}=-3,x_{2}=4
Evaluate
x^{2}=x+12
Move the expression to the left side
x^{2}-x-12=0
Factor the expression
More Steps
Evaluate
x^{2}-x-12
Rewrite the expression
x^{2}+\left(3-4\right)x-12
Calculate
x^{2}+3x-4x-12
Rewrite the expression
x\times x+x\times 3-4x-4\times 3
\text{Factor out }x\text{ from the expression}
x\left(x+3\right)-4x-4\times 3
\text{Factor out }-4\text{ from the expression}
x\left(x+3\right)-4\left(x+3\right)
\text{Factor out }x+3\text{ from the expression}
\left(x-4\right)\left(x+3\right)
\left(x-4\right)\left(x+3\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-4=0\\&x+3=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
\begin{align}&x=4\\&x+3=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0-3
Removing 0 doesn't change the value,so remove it from the expression
x=-3
\begin{align}&x=4\\&x=-3\end{align}
Solution
x_{1}=-3,x_{2}=4
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