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Question
-\frac{1}{2}x^{2}-4x-6
Factor the expression
-\frac{1}{2}\left(x+2\right)\left(x+6\right)
Evaluate
-\frac{1}{2}x^{2}-4x-6
Rewrite the expression
-\frac{1}{2}x^{2}-\frac{1}{2}\times 8x-\frac{1}{2}\times 12
\text{Factor out }-\frac{1}{2}\text{ from the expression}
-\frac{1}{2}\left(x^{2}+8x+12\right)
Solution
More Steps
Evaluate
x^{2}+8x+12
Rewrite the expression
x^{2}+\left(6+2\right)x+12
Calculate
x^{2}+6x+2x+12
Rewrite the expression
x\times x+x\times 6+2x+2\times 6
\text{Factor out }x\text{ from the expression}
x\left(x+6\right)+2x+2\times 6
\text{Factor out }2\text{ from the expression}
x\left(x+6\right)+2\left(x+6\right)
\text{Factor out }x+6\text{ from the expression}
\left(x+2\right)\left(x+6\right)
-\frac{1}{2}\left(x+2\right)\left(x+6\right)
Show Solutions
Find the roots
x_{1}=-6,x_{2}=-2
Evaluate
-\frac{1}{2}x^{2}-4x-6
To find the roots of the expression,set the expression equal to 0
-\frac{1}{2}x^{2}-4x-6=0
Factor the expression
More Steps
Evaluate
-\frac{1}{2}x^{2}-4x-6
Rewrite the expression
-\frac{1}{2}x^{2}-\frac{1}{2}\times 8x-\frac{1}{2}\times 12
\text{Factor out }-\frac{1}{2}\text{ from the expression}
-\frac{1}{2}\left(x^{2}+8x+12\right)
Factor the expression
More Steps
Evaluate
x^{2}+8x+12
Rewrite the expression
x^{2}+\left(6+2\right)x+12
Calculate
x^{2}+6x+2x+12
Rewrite the expression
x\times x+x\times 6+2x+2\times 6
\text{Factor out }x\text{ from the expression}
x\left(x+6\right)+2x+2\times 6
\text{Factor out }2\text{ from the expression}
x\left(x+6\right)+2\left(x+6\right)
\text{Factor out }x+6\text{ from the expression}
\left(x+2\right)\left(x+6\right)
-\frac{1}{2}\left(x+2\right)\left(x+6\right)
-\frac{1}{2}\left(x+2\right)\left(x+6\right)=0
Divide the terms
\left(x+2\right)\left(x+6\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x+2=0\\&x+6=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\\&x+6=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x+6=0
Move the constant to the right-hand side and change its sign
x=0-6
Removing 0 doesn't change the value,so remove it from the expression
x=-6
\begin{align}&x=-2\\&x=-6\end{align}
Solution
x_{1}=-6,x_{2}=-2
Show Solutions
