Solve the equation 3x-40+x^2=0

x^2+3x-40=0

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Answer

$x_1=5,\:x_2=-8$

Step by step solution

Problem

$x^2+3x-40=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=3$ and $c=-40$

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

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

$x=\frac{3\left(-1\right)\pm \sqrt{160+3^2}}{2}$
3

Multiply $-1$ times $3$

$x=\frac{-3\pm \sqrt{160+3^2}}{2}$
4

Calculate the power

$x=\frac{-3\pm \sqrt{160+9}}{2}$
5

Add the values $9$ and $160$

$x=\frac{-3\pm \sqrt{169}}{2}$
6

Calculate the power

$x=\frac{-3\pm 13}{2}$
7

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

$x_1=\frac{-3+ 13}{2}\:\:,\:\:x_2=\frac{-3- 13}{2}$
8

Simplifying

$x_1=5,\:x_2=-8$
9

We found that the two real solutions of the equation are

$x_1=5,\:x_2=-8$

Answer

$x_1=5,\:x_2=-8$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.21 seconds

Views:

97