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Question
-5x\times 8-4x^{2}-4x^{2}\times x^{2}
Simplify the expression
-40x-4x^{2}-4x^{4}
Evaluate
-5x\times 8-4x^{2}-4x^{2}\times x^{2}
Multiply the terms
-40x-4x^{2}-4x^{2}\times x^{2}
Solution
More Steps
Multiply the terms
-4x^{2}\times x^{2}
Multiply the terms with the same base by adding their exponents
-4x^{2+2}
Add the numbers
-4x^{4}
-40x-4x^{2}-4x^{4}
Show Solutions
Factor the expression
-4x\left(2+x\right)\left(x^{2}-2x+5\right)
Evaluate
-5x\times 8-4x^{2}-4x^{2}\times x^{2}
Multiply the terms
-40x-4x^{2}-4x^{2}\times x^{2}
Multiply
More Steps
Multiply the terms
4x^{2}\times x^{2}
Multiply the terms with the same base by adding their exponents
4x^{2+2}
Add the numbers
4x^{4}
-40x-4x^{2}-4x^{4}
Evaluate
-4x^{2}-40x-4x^{4}
Rewrite the expression
-4x\times x-4x\times 10-4x\times x^{3}
\text{Factor out }-4x\text{ from the expression}
-4x\left(x+10+x^{3}\right)
Solution
More Steps
Evaluate
x+10+x^{3}
Calculate
2x^{2}-4x+10+x^{3}-2x^{2}+5x
Rewrite the expression
2x^{2}-2\times 2x+2\times 5+x\times x^{2}-x\times 2x+x\times 5
\text{Factor out }2\text{ from the expression}
2\left(x^{2}-2x+5\right)+x\times x^{2}-x\times 2x+x\times 5
\text{Factor out }x\text{ from the expression}
2\left(x^{2}-2x+5\right)+x\left(x^{2}-2x+5\right)
\text{Factor out }x^{2}-2x+5\text{ from the expression}
\left(2+x\right)\left(x^{2}-2x+5\right)
-4x\left(2+x\right)\left(x^{2}-2x+5\right)
Show Solutions
Find the roots
x_{1}=1-2i,x_{2}=1+2i,x_{3}=-2,x_{4}=0
Evaluate
-5x\times 8-4x^{2}-4x^{2}\times x^{2}
To find the roots of the expression,set the expression equal to 0
-5x\times 8-4x^{2}-4x^{2}\times x^{2}=0
Multiply the terms
-40x-4x^{2}-4x^{2}\times x^{2}=0
Multiply
More Steps
Multiply the terms
4x^{2}\times x^{2}
Multiply the terms with the same base by adding their exponents
4x^{2+2}
Add the numbers
4x^{4}
-40x-4x^{2}-4x^{4}=0
Factor the expression
-4x\left(2+x\right)\left(x^{2}-2x+5\right)=0
Divide both sides
x\left(2+x\right)\left(x^{2}-2x+5\right)=0
\text{Separate the equation into }3\text{ possible cases}
\begin{align}&x=0\\&2+x=0\\&x^{2}-2x+5=0\end{align}
Solve the equation
More Steps
Evaluate
2+x=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=0\\&x=-2\\&x^{2}-2x+5=0\end{align}
Solve the equation
More Steps
Evaluate
x^{2}-2x+5=0
\text{Substitute a=}1\text{,b=}-2\text{ and c=}5\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 5}}{2}
Simplify the expression
More Steps
Evaluate
\left(-2\right)^{2}-4\times 5
Multiply the numbers
\left(-2\right)^{2}-20
Rewrite the expression
2^{2}-20
Evaluate the power
4-20
Subtract the numbers
-16
x=\frac{2\pm \sqrt{-16}}{2}
Simplify the radical expression
More Steps
Evaluate
\sqrt{-16}
Evaluate the power
\sqrt{16}\times \sqrt{-1}
Evaluate the power
\sqrt{16}\times i
Evaluate the square root
4i
x=\frac{2\pm 4i}{2}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{2+4i}{2}\\&x=\frac{2-4i}{2}\end{align}
Simplify the expression
\begin{align}&x=1+2i\\&x=\frac{2-4i}{2}\end{align}
Simplify the expression
\begin{align}&x=1+2i\\&x=1-2i\end{align}
\begin{align}&x=0\\&x=-2\\&x=1+2i\\&x=1-2i\end{align}
Solution
x_{1}=1-2i,x_{2}=1+2i,x_{3}=-2,x_{4}=0
Show Solutions
