Solve the equation x+2+x^2=113

x^2+x+2=113

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Answer

$x_1=10.0475,\:x_2=-11.0475$

Step by step solution

Problem

$x^2+x+2=113$
1

Subtract $2$ from both sides of the equation

$x+x^2=113-2$
2

Subtract the values $113$ and $-2$

$x+x^2=111$
3

Rewrite the equation

$-111+x+x^2=0$
4

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=1$ and $c=-111$

$x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
5

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

$x=\frac{-1\pm \sqrt{444+1^2}}{2}$
6

Calculate the power

$x=\frac{-1\pm \sqrt{444+1}}{2}$
7

Add the values $1$ and $444$

$x=\frac{-1\pm \sqrt{445}}{2}$
8

Calculate the power

$x=\frac{-1\pm 21.095}{2}$
9

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

$x_1=\frac{-1+ 21.095}{2}\:\:,\:\:x_2=\frac{-1- 21.095}{2}$
10

Simplifying

$x_1=10.0475,\:x_2=-11.0475$
11

We found that the two real solutions of the equation are

$x_1=10.0475,\:x_2=-11.0475$

Answer

$x_1=10.0475,\:x_2=-11.0475$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.27 seconds

Views:

73