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Question
2x^{2}+3x-14=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}=-\frac{7}{2},x_{2}=2
Alternative Form
x_{1}=-3.5,x_{2}=2
Evaluate
2x^{2}+3x-14=0
Factor the expression
More Steps
Evaluate
2x^{2}+3x-14
Rewrite the expression
2x^{2}+\left(7-4\right)x-14
Calculate
2x^{2}+7x-4x-14
Rewrite the expression
x\times 2x+x\times 7-2\times 2x-2\times 7
\text{Factor out }x\text{ from the expression}
x\left(2x+7\right)-2\times 2x-2\times 7
\text{Factor out }-2\text{ from the expression}
x\left(2x+7\right)-2\left(2x+7\right)
\text{Factor out }2x+7\text{ from the expression}
\left(x-2\right)\left(2x+7\right)
\left(x-2\right)\left(2x+7\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-2=0\\&2x+7=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=2\\&2x+7=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
2x+7=0
Move the constant to the right-hand side and change its sign
2x=0-7
Removing 0 doesn't change the value,so remove it from the expression
2x=-7
Divide both sides
\frac{2x}{2}=\frac{-7}{2}
Divide the numbers
x=\frac{-7}{2}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x=-\frac{7}{2}
\begin{align}&x=2\\&x=-\frac{7}{2}\end{align}
Solution
x_{1}=-\frac{7}{2},x_{2}=2
Alternative Form
x_{1}=-3.5,x_{2}=2
Show Solutions
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