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Question
5x^{2}-7x+2
Factor the expression
\left(x-1\right)\left(5x-2\right)
Evaluate
5x^{2}-7x+2
Rewrite the expression
5x^{2}+\left(-2-5\right)x+2
Calculate
5x^{2}-2x-5x+2
Rewrite the expression
x\times 5x-x\times 2-5x+2
\text{Factor out }x\text{ from the expression}
x\left(5x-2\right)-5x+2
\text{Factor out }-1\text{ from the expression}
x\left(5x-2\right)-\left(5x-2\right)
Solution
\left(x-1\right)\left(5x-2\right)
Show Solutions
Find the roots
x_{1}=\frac{2}{5},x_{2}=1
Alternative Form
x_{1}=0.4,x_{2}=1
Evaluate
5x^{2}-7x+2
To find the roots of the expression,set the expression equal to 0
5x^{2}-7x+2=0
Factor the expression
More Steps
Evaluate
5x^{2}-7x+2
Rewrite the expression
5x^{2}+\left(-2-5\right)x+2
Calculate
5x^{2}-2x-5x+2
Rewrite the expression
x\times 5x-x\times 2-5x+2
\text{Factor out }x\text{ from the expression}
x\left(5x-2\right)-5x+2
\text{Factor out }-1\text{ from the expression}
x\left(5x-2\right)-\left(5x-2\right)
\text{Factor out }5x-2\text{ from the expression}
\left(x-1\right)\left(5x-2\right)
\left(x-1\right)\left(5x-2\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-1=0\\&5x-2=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\\&5x-2=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
5x-2=0
Move the constant to the right-hand side and change its sign
5x=0+2
Removing 0 doesn't change the value,so remove it from the expression
5x=2
Divide both sides
\frac{5x}{5}=\frac{2}{5}
Divide the numbers
x=\frac{2}{5}
\begin{align}&x=1\\&x=\frac{2}{5}\end{align}
Solution
x_{1}=\frac{2}{5},x_{2}=1
Alternative Form
x_{1}=0.4,x_{2}=1
Show Solutions
