Question

How do I solve this equation and check the solutions?

Answer 1

{-6}

Explanation:

Step 1 Raise both sides of the equation to the index of the radical in the case 2

`(√(2x+13) )^(2) =(x+7)^(2)`

`2x + 13 = (x+7)(x+7)`

`2x +13 = x^(2) + 14x + 49\\0=x^(2) +12x+36`

Step 2 Factor

(x + 6)(x + 6) = 0

x + 6 = 0

x = - 6

Step 3 Check -6

`√(2(-6)+13) = -6 + 7\\√(-12+13) = 1\\√(1) = 1\\1 = 1`