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Question
x^{2}-5x+6=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
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x_{1}=2,x_{2}=3
Evaluate
x^{2}-5x+6=0
Factor the expression
More Steps
Evaluate
x^{2}-5x+6
Rewrite the expression
x^{2}+\left(-2-3\right)x+6
Calculate
x^{2}-2x-3x+6
Rewrite the expression
x\times x-x\times 2-3x+3\times 2
\text{Factor out }x\text{ from the expression}
x\left(x-2\right)-3x+3\times 2
\text{Factor out }-3\text{ from the expression}
x\left(x-2\right)-3\left(x-2\right)
\text{Factor out }x-2\text{ from the expression}
\left(x-3\right)\left(x-2\right)
\left(x-3\right)\left(x-2\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-3=0\\&x-2=0\end{align}
\text{Solve the equation for }x
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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=3\\&x-2=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
\begin{align}&x=3\\&x=2\end{align}
Solution
x_{1}=2,x_{2}=3
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