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Question
x^{2}-4x-36
Find the roots
x_{1}=2-2\sqrt{10},x_{2}=2+2\sqrt{10}
Alternative Form
x_{1}\approx -4.324555,x_{2}\approx 8.324555
Evaluate
x^{2}-4x-36
To find the roots of the expression,set the expression equal to 0
x^{2}-4x-36=0
\text{Substitute a=}1\text{,b=}-4\text{ and c=}-36\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\left(-36\right)}}{2}
Simplify the expression
More Steps
Evaluate
\left(-4\right)^{2}-4\left(-36\right)
Multiply the numbers
More Steps
Evaluate
4\left(-36\right)
Multiplying or dividing an odd number of negative terms equals a negative
-4\times 36
Multiply the numbers
-144
\left(-4\right)^{2}-\left(-144\right)
Rewrite the expression
4^{2}-\left(-144\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4^{2}+144
Evaluate the power
16+144
Add the numbers
160
x=\frac{4\pm \sqrt{160}}{2}
Simplify the radical expression
More Steps
Evaluate
\sqrt{160}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{16\times 10}
\text{Write the number in exponential form with the base of }4
\sqrt{4^{2}\times 10}
The root of a product is equal to the product of the roots of each factor
\sqrt{4^{2}}\times \sqrt{10}
\text{Reduce the index of the radical and exponent with }2
4\sqrt{10}
x=\frac{4\pm 4\sqrt{10}}{2}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{4+4\sqrt{10}}{2}\\&x=\frac{4-4\sqrt{10}}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{4+4\sqrt{10}}{2}
Divide the terms
More Steps
Evaluate
\frac{4+4\sqrt{10}}{2}
Rewrite the expression
\frac{2\left(2+2\sqrt{10}\right)}{2}
Reduce the fraction
2+2\sqrt{10}
x=2+2\sqrt{10}
\begin{align}&x=2+2\sqrt{10}\\&x=\frac{4-4\sqrt{10}}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{4-4\sqrt{10}}{2}
Divide the terms
More Steps
Evaluate
\frac{4-4\sqrt{10}}{2}
Rewrite the expression
\frac{2\left(2-2\sqrt{10}\right)}{2}
Reduce the fraction
2-2\sqrt{10}
x=2-2\sqrt{10}
\begin{align}&x=2+2\sqrt{10}\\&x=2-2\sqrt{10}\end{align}
Solution
x_{1}=2-2\sqrt{10},x_{2}=2+2\sqrt{10}
Alternative Form
x_{1}\approx -4.324555,x_{2}\approx 8.324555
Show Solutions
