Solve the equation 7x-10+-1x^2=0

-x^2+7x-10=0

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Answer

$x_1=2,\:x_2=5$

Step by step solution

Problem

$-x^2+7x-10=0$
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 $c=-10$

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

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

$x=\frac{7\left(-1\right)\pm \sqrt{7^2-10\left(-1\right)\left(-4\right)}}{-1\cdot 2}$
3

Multiply $-1$ times $7$

$x=\frac{-7\pm \sqrt{7^2-40}}{-2}$
4

Calculate the power

$x=\frac{-7\pm \sqrt{49-40}}{-2}$
5

Add the values $49$ and $-40$

$x=\frac{-7\pm \sqrt{9}}{-2}$
6

Calculate the power

$x=\frac{-7\pm 3}{-2}$
7

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

$x_1=\frac{-7+ 3}{-2}\:\:,\:\:x_2=\frac{-7- 3}{-2}$
8

Simplifying

$x_1=2,\:x_2=5$
9

We found that the two real solutions of the equation are

$x_1=2,\:x_2=5$

Answer

$x_1=2,\:x_2=5$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.22 seconds

Views:

176