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Question
x^{2}-7x=10x-70
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}=7,x_{2}=10
Evaluate
x^{2}-7x=10x-70
Move the expression to the left side
x^{2}-17x+70=0
Factor the expression
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Evaluate
x^{2}-17x+70
Rewrite the expression
x^{2}+\left(-7-10\right)x+70
Calculate
x^{2}-7x-10x+70
Rewrite the expression
x\times x-x\times 7-10x+10\times 7
\text{Factor out }x\text{ from the expression}
x\left(x-7\right)-10x+10\times 7
\text{Factor out }-10\text{ from the expression}
x\left(x-7\right)-10\left(x-7\right)
\text{Factor out }x-7\text{ from the expression}
\left(x-10\right)\left(x-7\right)
\left(x-10\right)\left(x-7\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-10=0\\&x-7=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-10=0
Move the constant to the right-hand side and change its sign
x=0+10
Removing 0 doesn't change the value,so remove it from the expression
x=10
\begin{align}&x=10\\&x-7=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-7=0
Move the constant to the right-hand side and change its sign
x=0+7
Removing 0 doesn't change the value,so remove it from the expression
x=7
\begin{align}&x=10\\&x=7\end{align}
Solution
x_{1}=7,x_{2}=10
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