Verified answer

1+√(x+7)=√(2x+7)

(1+√(x+7))²=(√(2x+7))²

1+x+7=2x+7

x+8=2x+7

x-x+8=2x-x+7

8=x+7

8-7=x+7-7

1=x

Check:

1+√(x+7)=√(2x+7)

1+√(1+7)=√(2(1)+7)

1+√8=√(2+7)

1+√8=√9

1+√8≠3

Ø (no solution)

This should be the answer. However, I may be incorrect.

sq. the two sides: [a million + ?(x + 7)]² = [?(2x + 7)]² Simplify: a million + 2?(x + 7) + (x + 7) = 2x + 7 Simplify extra: x + 8 + 2?(x + 7) = 2x + 7 Subtract x + 8 from the two sides: 2?(x + 7) = x – a million sq. the two sides: [2?(x + 7)]² = (x – a million)² Simplify: 4(x + 7) = x² – 2x + a million Distribute: 4x + 28 = x² – 2x + a million Subtract 4x + 28 from the two sides: x² – 6x – 27 = 0 element: (x – 9)(x + 3) = 0 sparkling up the ensuing equations: x = –3, 9 you're able to desire to constantly verify radical equations via plugging your recommendations into the unique equation. for this reason, x = –3 is an extraneous answer because it would not artwork. for this reason, the respond is: x = 9