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Question
x^{2}-8x+170
Find the roots
x_{1}=4-\sqrt{154}\times i,x_{2}=4+\sqrt{154}\times i
Alternative Form
x_{1}\approx 4-12.409674i,x_{2}\approx 4+12.409674i
Evaluate
x^{2}-8x+170
To find the roots of the expression,set the expression equal to 0
x^{2}-8x+170=0
\text{Substitute a=}1\text{,b=}-8\text{ and c=}170\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{8\pm \sqrt{\left(-8\right)^{2}-4\times 170}}{2}
Simplify the expression
More Steps
Evaluate
\left(-8\right)^{2}-4\times 170
Multiply the numbers
\left(-8\right)^{2}-680
Rewrite the expression
8^{2}-680
Evaluate the power
64-680
Subtract the numbers
-616
x=\frac{8\pm \sqrt{-616}}{2}
Simplify the radical expression
More Steps
Evaluate
\sqrt{-616}
Evaluate the power
\sqrt{616}\times \sqrt{-1}
Evaluate the power
\sqrt{616}\times i
Evaluate the power
More Steps
Evaluate
\sqrt{616}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 154}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 154}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{154}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{154}
2\sqrt{154}\times i
x=\frac{8\pm 2\sqrt{154}\times i}{2}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{8+2\sqrt{154}\times i}{2}\\&x=\frac{8-2\sqrt{154}\times i}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{8+2\sqrt{154}\times i}{2}
Divide the terms
More Steps
Evaluate
\frac{8+2\sqrt{154}\times i}{2}
Rewrite the expression
\frac{2\left(4+\sqrt{154}\times i\right)}{2}
Reduce the fraction
4+\sqrt{154}\times i
x=4+\sqrt{154}\times i
\begin{align}&x=4+\sqrt{154}\times i\\&x=\frac{8-2\sqrt{154}\times i}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{8-2\sqrt{154}\times i}{2}
Divide the terms
More Steps
Evaluate
\frac{8-2\sqrt{154}\times i}{2}
Rewrite the expression
\frac{2\left(4-\sqrt{154}\times i\right)}{2}
Reduce the fraction
4-\sqrt{154}\times i
x=4-\sqrt{154}\times i
\begin{align}&x=4+\sqrt{154}\times i\\&x=4-\sqrt{154}\times i\end{align}
Solution
x_{1}=4-\sqrt{154}\times i,x_{2}=4+\sqrt{154}\times i
Alternative Form
x_{1}\approx 4-12.409674i,x_{2}\approx 4+12.409674i
Show Solutions
