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Question
2x^{2}+13x-7
Factor the expression
\left(x+7\right)\left(2x-1\right)
Evaluate
2x^{2}+13x-7
Rewrite the expression
2x^{2}+\left(-1+14\right)x-7
Calculate
2x^{2}-x+14x-7
Rewrite the expression
x\times 2x-x+7\times 2x-7
\text{Factor out }x\text{ from the expression}
x\left(2x-1\right)+7\times 2x-7
\text{Factor out }7\text{ from the expression}
x\left(2x-1\right)+7\left(2x-1\right)
Solution
\left(x+7\right)\left(2x-1\right)
Show Solutions
Find the roots
x_{1}=-7,x_{2}=\frac{1}{2}
Alternative Form
x_{1}=-7,x_{2}=0.5
Evaluate
2x^{2}+13x-7
To find the roots of the expression,set the expression equal to 0
2x^{2}+13x-7=0
Factor the expression
More Steps
Evaluate
2x^{2}+13x-7
Rewrite the expression
2x^{2}+\left(-1+14\right)x-7
Calculate
2x^{2}-x+14x-7
Rewrite the expression
x\times 2x-x+7\times 2x-7
\text{Factor out }x\text{ from the expression}
x\left(2x-1\right)+7\times 2x-7
\text{Factor out }7\text{ from the expression}
x\left(2x-1\right)+7\left(2x-1\right)
\text{Factor out }2x-1\text{ from the expression}
\left(x+7\right)\left(2x-1\right)
\left(x+7\right)\left(2x-1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x+7=0\\&2x-1=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=-7\\&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=-7\\&x=\frac{1}{2}\end{align}
Solution
x_{1}=-7,x_{2}=\frac{1}{2}
Alternative Form
x_{1}=-7,x_{2}=0.5
Show Solutions
