Solve the inequality x-12+x^2<0

x^2+x-12<0

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$-4<x<3$

Step by step solution

Problem

$x^2+x-12<0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=1$ and $c=-12$

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

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

$x=\frac{-1\pm \sqrt{48+1^2}}{2}$
3

Calculate the power

$x=\frac{-1\pm \sqrt{48+1}}{2}$
4

Add the values $1$ and $48$

$x=\frac{-1\pm \sqrt{49}}{2}$
5

Calculate the power

$x=\frac{-1\pm 7}{2}$
6

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

$x_1=\frac{-1+ 7}{2}\:\:,\:\:x_2=\frac{-1- 7}{2}$
7

Simplifying

$x_1=3,\:x_2=-4$
8

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

$-4<x<3$

Answer

$-4<x<3$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.26 seconds

Views:

68