This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.
ScanSolve AI Answer
To find the value of x in the equation sqrt(x+1) + sqrt(x-5) = 8, we will isolate one radical, square both sides, and then repeat the process. Step 1: Isolate one of the square root terms. Subtract sqrt(x-5) from both sides: sqrt(x+1) = 8 - sqrt(x-5) Step 2: Square both sides of the equation. (sqrt(x+1))^2 = (8 - sqrt(x-5))^2 x+1 = 8^2 - 2(8)sqrt(x-5) + (sqrt(x-5))^2 x+1 = 64 - 16sqrt(x-5) + (x-5) Step 3: Simplify the equation. x+1 = x + 59 - 16sqrt(x-5) Step 4: Isolate the remaining square root term. Subtract x from both sides: 1 = 59 - 16sqrt(x-5) Subtract 59 from both sides: 1 - 59 = -16sqrt(x-5) -58 = -16sqrt(x-5) Divide by -16: (-58)/(-16) = sqrt(x-5) (29)/(8) = sqrt(x-5) Step 5: Square both sides again. ((29)/(8))^2 = (sqrt(x-5))^2 (29^2)/(8^2) = x-5 (841)/(64) = x-5 Step 6: Solve for x. Add 5 to both sides: x = (841)/(64) + 5 To add, find a common denominator: x = (841)/(64) + (5 × 64)/(64) x = (841)/(64) + (320)/(64) x = (841 + 320)/(64) x = (1161)/(64) Step 7: Check the solution. Substitute x = (1161)/(64) into the original equation: sqrt((1161)/(64)+1) + sqrt((1161)/(64)-5) = 8 sqrt((1161+64)/(64)) + sqrt((1161-320)/(64)) = 8 sqrt((1225)/(64)) + sqrt((841)/(64)) = 8 sqrt(1225)sqrt(64) + sqrt(841)sqrt(64) = 8 (35)/(8) + (29)/(8) = 8 (35+29)/(8) = 8 (64)/(8) = 8 8 = 8 The solution is correct. The value of x is (1161)/(64).