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Question
2x^{2}-3x+1=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}=\frac{1}{2},x_{2}=1
Alternative Form
x_{1}=0.5,x_{2}=1
Evaluate
2x^{2}-3x+1=0
Factor the expression
More Steps
Evaluate
2x^{2}-3x+1
Rewrite the expression
2x^{2}+\left(-1-2\right)x+1
Calculate
2x^{2}-x-2x+1
Rewrite the expression
x\times 2x-x-2x+1
\text{Factor out }x\text{ from the expression}
x\left(2x-1\right)-2x+1
\text{Factor out }-1\text{ from the expression}
x\left(2x-1\right)-\left(2x-1\right)
\text{Factor out }2x-1\text{ from the expression}
\left(x-1\right)\left(2x-1\right)
\left(x-1\right)\left(2x-1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-1=0\\&2x-1=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
\begin{align}&x=1\\&2x-1=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
2x-1=0
Move the constant to the right-hand side and change its sign
2x=0+1
Removing 0 doesn't change the value,so remove it from the expression
2x=1
Divide both sides
\frac{2x}{2}=\frac{1}{2}
Divide the numbers
x=\frac{1}{2}
\begin{align}&x=1\\&x=\frac{1}{2}\end{align}
Solution
x_{1}=\frac{1}{2},x_{2}=1
Alternative Form
x_{1}=0.5,x_{2}=1
Show Solutions
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