Solve x=frac{-10+sqrt{10^2-4*5*1}}{2*5}

$$x = \frac{ -10+ \sqrt{ { 10 }^{ 2 } -4 \cdot 5 \cdot 1 } }{ 2 \cdot 5 }$$

Solve for x

$$x=\frac{2\sqrt{5}}{5}-1\approx -0.105572809$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$x=\frac{-10+\sqrt{100-4\times 5\times 1}}{2\times 5}$$

Multiply 4 and 5 to get 20.

$$x=\frac{-10+\sqrt{100-20\times 1}}{2\times 5}$$

Multiply 20 and 1 to get 20.

$$x=\frac{-10+\sqrt{100-20}}{2\times 5}$$

Subtract 20 from 100 to get 80.

$$x=\frac{-10+\sqrt{80}}{2\times 5}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$x=\frac{-10+4\sqrt{5}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$x=\frac{-10+4\sqrt{5}}{10}$$

Divide each term of -10+4\sqrt{5} by 10 to get -1+\frac{2}{5}\sqrt{5}.

$$x=-1+\frac{2}{5}\sqrt{5}$$

Assign x

$$x≔\frac{2\sqrt{5}}{5}-1$$