hours x 2 ,5, 7 Charge, y ($) 20, 50 ,70 Write an equation that expresses y in terms of x. please answer as soon as possible this is due today and I don't understand this question

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Ответ:

KAMOO3X

04.09.2022

Mathematics

Given:

The equation is:

x^2+5x=2

To find:

The solution of the given equation by completing the square.

Solution:

We have,

x^2+5x=2

We need to add the square of half of the coefficient of x on both sides.

Adding $\left(\dfrac{5}{2}\right)^2$ on both sides, we get

$x^2+5x+\left(\dfrac{5}{2}\right)^2=2+\left(\dfrac{5}{2}\right)^2$

$\left(x+\dfrac{5}{2}\right)^2=2+\dfrac{25}{4}$

$\left(x+\dfrac{5}{2}\right)^2=\dfrac{8+25}{4}$

$\left(x+\dfrac{5}{2}\right)^2=\dfrac{33}{4}$

Taking square root on both sides, we get

$x+\dfrac{5}{2}=\pm \sqrt{\dfrac{33}{4}}$

$x=\pm \dfrac{\sqrt{33}}{2}-\dfrac{5}{2}$

$x=\dfrac{\pm \sqrt{33}-5}{2}$

$x=\dfrac{\sqrt{33}-5}{2}$ and $x=\dfrac{-\sqrt{33}-5}{2}$

Therefore, the solutions of the given equation are $x=\dfrac{\sqrt{33}-5}{2}$ and $x=\dfrac{-\sqrt{33}-5}{2}$ .

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