Question

(3x −5)^2 =(? + ?? +25)

Answer 1

x = 3.556 or
`(32)/(9)`

Explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:

(3*x-5)^2-((x+x+25))=0

Evaluate:

`(3x-5)^(2)` =
`9x^(2) -30x+25`

Pull like factors:

9x^2 - 32x = x • (9x - 32)

x • (9x - 32) = 0

Remember roots of a product:

A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately. In other words, we are going to solve as many equations as there are terms in the product. Any solution of term = 0 solves product = 0 as well.

Solve : 9x - 32 = 0

Add 32 to both sides of the equation :

9x = 32

Divide both sides of the equation by 9:

x = 32/9 = 3.556