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# Solve the inequality -1x-2x^2+1%0

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## Answer

$0.5\geq x\geq -1$

## Step by step solution

Problem

$1-x-2x^2\geq 0$
1

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

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

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

$x=\frac{-1\left(-1\right)\pm \sqrt{8+{\left(-1\right)}^2}}{-2\cdot 2}$
3

Multiply $-1$ times $-1$

$x=\frac{1\pm \sqrt{8+{\left(-1\right)}^2}}{-4}$
4

Calculate the power

$x=\frac{1\pm \sqrt{8+1}}{-4}$
5

Add the values $1$ and $8$

$x=\frac{1\pm \sqrt{9}}{-4}$
6

Calculate the power

$x=\frac{1\pm 3}{-4}$
7

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

$x_1=\frac{1+ 3}{-4}\:\:,\:\:x_2=\frac{1- 3}{-4}$
8

Simplifying

$x_1=-1,\:x_2=0.5$
9

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

$0.5\geq x\geq -1$

## Answer

$0.5\geq x\geq -1$

### Main topic:

Quadratic formula

0.19 seconds

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