Solve the inequality -4x+2+2x^2%0

2x^2-4x+2\geq 0

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Answer

$1\geq x\geq 1$

Step by step solution

Problem

$2x^2-4x+2\geq 0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=2$, $b=-4$ and $c=2$

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

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

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

Multiply $-1$ times $-4$

$x=\frac{4\pm \sqrt{{\left(-4\right)}^2-16}}{4}$
4

Calculate the power

$x=\frac{4\pm \sqrt{16-16}}{4}$
5

Add the values $16$ and $-16$

$x=\frac{4\pm \sqrt{0}}{4}$
6

Calculate the power

$x=\frac{4\pm 0}{4}$
7

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

$x_1=\frac{4+ 0}{4}\:\:,\:\:x_2=\frac{4- 0}{4}$
8

Simplifying

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

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

$1\geq x\geq 1$

Answer

$1\geq x\geq 1$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.2 seconds

Views:

177