Solve the equation 7x+3+x^2=0

x^2+7x+3=0

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Answer

$x_1=-0.4586,\:x_2=-6.5414$

Step by step solution

Problem

$x^2+7x+3=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=7$ and $c=3$

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

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

$x=\frac{7\left(-1\right)\pm \sqrt{7^2-12}}{2}$
3

Multiply $-1$ times $7$

$x=\frac{-7\pm \sqrt{7^2-12}}{2}$
4

Calculate the power

$x=\frac{-7\pm \sqrt{49-12}}{2}$
5

Add the values $49$ and $-12$

$x=\frac{-7\pm \sqrt{37}}{2}$
6

Calculate the power

$x=\frac{-7\pm \sqrt{36}}{2}$
7

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

$x_1=\frac{-7+ \sqrt{36}}{2}\:\:,\:\:x_2=\frac{-7- \sqrt{36}}{2}$
8

Simplifying

$x_1=-0.4586,\:x_2=-6.5414$
9

We found that the two real solutions of the equation are

$x_1=-0.4586,\:x_2=-6.5414$

Answer

$x_1=-0.4586,\:x_2=-6.5414$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.22 seconds

Views:

89