Question

Please help explain how to solve problem 16?

Answer 1

Here is the problem.....√(15x + 10) = 2x+3

to remove the square root, we do the opposite which is to square everything.

(√(15x + 10))² = (2x + 3)²      (the square negates the square root)
15x + 10 = (2x +3)(2x + 3)    (use the distributive property to continue)
15x + 10 = 4x² + 6x + 6x + 9  (combine like terms)
15x + 10 = 4x² + 12x + 9      (subtract 15x and 10 from each side)
-15x - 10          -15x - 10
0 = 4x² - 3x - 1                      (factor completely)
(x - 1) (4x + 1)                    (set each to equal 0)

x - 1 = 0                4x + 1 = 0
x = 1                      4x = -1
                               x = -1/4

place both into the equation to check for reasonableness...we see the negative number is not reasonable, but the x value of 1 is a solution.

answer is 1