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Question
-x^{2}+16x-63=0
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
More methods
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x_{1}=7,x_{2}=9
Evaluate
-x^{2}+16x-63=0
Factor the expression
More Steps
Evaluate
-x^{2}+16x-63
Rewrite the expression
-x^{2}+\left(7+9\right)x-63
Calculate
-x^{2}+7x+9x-63
Rewrite the expression
-x\times x+x\times 7+9x-9\times 7
\text{Factor out }-x\text{ from the expression}
-x\left(x-7\right)+9x-9\times 7
\text{Factor out }9\text{ from the expression}
-x\left(x-7\right)+9\left(x-7\right)
\text{Factor out }x-7\text{ from the expression}
\left(-x+9\right)\left(x-7\right)
\left(-x+9\right)\left(x-7\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&-x+9=0\\&x-7=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
-x+9=0
Move the constant to the right-hand side and change its sign
-x=0-9
Removing 0 doesn't change the value,so remove it from the expression
-x=-9
Change the signs on both sides of the equation
x=9
\begin{align}&x=9\\&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=9\\&x=7\end{align}
Solution
x_{1}=7,x_{2}=9
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