Solve the equation -7x+6+x^2=0

x^2-7x+6=0

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Answer

$x_1=6,\:x_2=1$

Step by step solution

Problem

$x^2-7x+6=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=-7$ 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

$x=\frac{-7\left(-1\right)\pm \sqrt{{\left(-7\right)}^2-24}}{2}$
3

Multiply $-1$ times $-7$

$x=\frac{7\pm \sqrt{{\left(-7\right)}^2-24}}{2}$
4

Calculate the power

$x=\frac{7\pm \sqrt{49-24}}{2}$
5

Add the values $49$ and $-24$

$x=\frac{7\pm \sqrt{25}}{2}$
6

Calculate the power

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

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

$x_1=\frac{7+ 5}{2}\:\:,\:\:x_2=\frac{7- 5}{2}$
8

Simplifying

$x_1=6,\:x_2=1$
9

We found that the two real solutions of the equation are

$x_1=6,\:x_2=1$

Answer

$x_1=6,\:x_2=1$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.82 seconds

Views:

138