Question

How do I solve this equation and check the solutions?

Answer 1

Answer:

{-6}

Step-by-step explanation:

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

$(\sqrt{2x+13} )^{2} =(x+7)^{2}$

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

$2x +13 = x^{2} + 14x + 49\\0=x^{2} +12x+36$

Step 2 Factor

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

x + 6 = 0

x = - 6

Step 3 Check -6

$\sqrt{2(-6)+13} = -6 + 7\\\sqrt{-12+13} = 1\\\sqrt{1} = 1\\1 = 1$