Solve the equation 8x+8+x^2=0

x^2+8x+8=0

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Answer

$x_1=-1.1716,\:x_2=-6.8284$

Step by step solution

Problem

$x^2+8x+8=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=8$ and $c=8$

$x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
2

Substituting the values of the coefficients of the equation in the quadratic formula

$x=\frac{8\left(-1\right)\pm \sqrt{8^2-32}}{2}$
3

Multiply $-1$ times $8$

$x=\frac{-8\pm \sqrt{8^2-32}}{2}$
4

Calculate the power

$x=\frac{-8\pm \sqrt{64-32}}{2}$
5

Add the values $64$ and $-32$

$x=\frac{-8\pm \sqrt{32}}{2}$
6

Calculate the power

$x=\frac{-8\pm \sqrt{32}}{2}$
7

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x_1=\frac{-8+ \sqrt{32}}{2}\:\:,\:\:x_2=\frac{-8- \sqrt{32}}{2}$
8

Simplifying

$x_1=-1.1716,\:x_2=-6.8284$
9

We found that the two real solutions of the equation are

$x_1=-1.1716,\:x_2=-6.8284$

Answer

$x_1=-1.1716,\:x_2=-6.8284$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.88 seconds

Views:

89