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Question
-5x^{2}+10x+2
Find the roots
x_{1}=\frac{5-\sqrt{35}}{5},x_{2}=\frac{5+\sqrt{35}}{5}
Alternative Form
x_{1}\approx -0.183216,x_{2}\approx 2.183216
Evaluate
-5x^{2}+10x+2
To find the roots of the expression,set the expression equal to 0
-5x^{2}+10x+2=0
Multiply both sides
5x^{2}-10x-2=0
\text{Substitute a=}5\text{,b=}-10\text{ and c=}-2\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{10\pm \sqrt{\left(-10\right)^{2}-4\times 5\left(-2\right)}}{2\times 5}
Simplify the expression
x=\frac{10\pm \sqrt{\left(-10\right)^{2}-4\times 5\left(-2\right)}}{10}
Simplify the expression
More Steps
Evaluate
\left(-10\right)^{2}-4\times 5\left(-2\right)
Multiply
More Steps
Multiply the terms
4\times 5\left(-2\right)
Rewrite the expression
-4\times 5\times 2
Multiply the terms
-40
\left(-10\right)^{2}-\left(-40\right)
Rewrite the expression
10^{2}-\left(-40\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
10^{2}+40
Evaluate the power
100+40
Add the numbers
140
x=\frac{10\pm \sqrt{140}}{10}
Simplify the radical expression
More Steps
Evaluate
\sqrt{140}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 35}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 35}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{35}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{35}
x=\frac{10\pm 2\sqrt{35}}{10}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{10+2\sqrt{35}}{10}\\&x=\frac{10-2\sqrt{35}}{10}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{10+2\sqrt{35}}{10}
Divide the terms
More Steps
Evaluate
\frac{10+2\sqrt{35}}{10}
Rewrite the expression
\frac{2\left(5+\sqrt{35}\right)}{10}
\text{Cancel out the common factor }2
\frac{5+\sqrt{35}}{5}
x=\frac{5+\sqrt{35}}{5}
\begin{align}&x=\frac{5+\sqrt{35}}{5}\\&x=\frac{10-2\sqrt{35}}{10}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{10-2\sqrt{35}}{10}
Divide the terms
More Steps
Evaluate
\frac{10-2\sqrt{35}}{10}
Rewrite the expression
\frac{2\left(5-\sqrt{35}\right)}{10}
\text{Cancel out the common factor }2
\frac{5-\sqrt{35}}{5}
x=\frac{5-\sqrt{35}}{5}
\begin{align}&x=\frac{5+\sqrt{35}}{5}\\&x=\frac{5-\sqrt{35}}{5}\end{align}
Solution
x_{1}=\frac{5-\sqrt{35}}{5},x_{2}=\frac{5+\sqrt{35}}{5}
Alternative Form
x_{1}\approx -0.183216,x_{2}\approx 2.183216
Show Solutions
