Solve the inequality -2x-15+x^2<0

{x^2-2x-15}<{0}

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Answer

$-3<x<5$

Step by step solution

Problem

${x^2-2x-15}<{0}$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=-2$ and $c=-15$

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

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

$x=\frac{-2\left(-1\right)\pm \sqrt{60+{\left(-2\right)}^2}}{2}$
3

Multiply $-1$ times $-2$

$x=\frac{2\pm \sqrt{60+{\left(-2\right)}^2}}{2}$
4

Calculate the power

$x=\frac{2\pm \sqrt{60+4}}{2}$
5

Add the values $4$ and $60$

$x=\frac{2\pm \sqrt{64}}{2}$
6

Calculate the power

$x=\frac{2\pm 8}{2}$
7

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

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

Simplifying

$x_1=5,\:x_2=-3$
9

Applying the quadratic formula we obtained the two solutions $x_1$ and $x_2$, with which we write the solution interval

$-3<x<5$

Answer

$-3<x<5$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.19 seconds

Views:

74