Answers and Step-by-step explanations
13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32
Move all the terms to one side: x^2 - 12x + 36 = 0
Factorize: (x - 6)^2 = 0 ⇒ x = 6
14. Move one of the roots to one side: ![-\sqrt{2x-1} =\sqrt{3x-12}](https://tex.z-dn.net/?f=-%5Csqrt%7B2x-1%7D%20%3D%5Csqrt%7B3x-12%7D)
Square both sides: 2x - 1 = 3x - 12
Solve for x: x = 11
15. Subtract 4 from both sides: x - 4 = ![2\sqrt{x-4}](https://tex.z-dn.net/?f=2%5Csqrt%7Bx-4%7D)
Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16
Move all the terms to one side: x^2 - 12x + 32 = 0
Factorize: (x - 4)(x - 8) = 0 ⇒ x = 4 or x = 8
16. Square both sides: x^2 - 4x + 4 = 9x - 36
Move all the terms to one side: x^2 - 13x + 40 = 0
Factorize: (x - 5)(x - 8) = 0 ⇒ x = 5 or x = 8
Hope this helps!