Solve the equation -1x-6+12x^2=0

12x^2-x-6=0

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Answer

$x_1=0.75,\:x_2=-0.6667$

Step by step solution

Problem

$12x^2-x-6=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=12$, $b=-1$ and $c=-6$

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

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

$x=\frac{-1\left(-1\right)\pm \sqrt{{\left(-1\right)}^2-6\cdot 12\left(-4\right)}}{12\cdot 2}$
3

Multiply $-1$ times $-1$

$x=\frac{1\pm \sqrt{288+{\left(-1\right)}^2}}{24}$
4

Calculate the power

$x=\frac{1\pm \sqrt{288+1}}{24}$
5

Add the values $1$ and $288$

$x=\frac{1\pm \sqrt{289}}{24}$
6

Calculate the power

$x=\frac{1\pm 17}{24}$
7

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

$x_1=\frac{1+ 17}{24}\:\:,\:\:x_2=\frac{1- 17}{24}$
8

Simplifying

$x_1=0.75,\:x_2=-0.6667$
9

We found that the two real solutions of the equation are

$x_1=0.75,\:x_2=-0.6667$

Answer

$x_1=0.75,\:x_2=-0.6667$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.23 seconds

Views:

149