Solve the inequality -5x+6+x^2%0

x^2-5x+6\geq 0

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Answer

$2\geq x\geq 3$

Step by step solution

Problem

$x^2-5x+6\geq 0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=-5$ 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

$x=\frac{-5\left(-1\right)\pm \sqrt{{\left(-5\right)}^2-24}}{2}$
3

Multiply $-1$ times $-5$

$x=\frac{5\pm \sqrt{{\left(-5\right)}^2-24}}{2}$
4

Calculate the power

$x=\frac{5\pm \sqrt{25-24}}{2}$
5

Add the values $25$ and $-24$

$x=\frac{5\pm \sqrt{1}}{2}$
6

Calculate the power

$x=\frac{5\pm 1}{2}$
7

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

$x_1=\frac{5+ 1}{2}\:\:,\:\:x_2=\frac{5- 1}{2}$
8

Simplifying

$x_1=3,\:x_2=2$
9

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

$2\geq x\geq 3$

Answer

$2\geq x\geq 3$

Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.24 seconds

Views:

164