Solve for x:
81 = (x - 3)^2 + (x + 5)^2
81 = (x - 3)^2 + (x + 5)^2 is equivalent to (x - 3)^2 + (x + 5)^2 = 81:
(x - 3)^2 + (x + 5)^2 = 81
Expand out terms of the left hand side:
2 x^2 + 4 x + 34 = 81
Divide both sides by 2:
x^2 + 2 x + 17 = 81/2
Subtract 17 from both sides:
x^2 + 2 x = 47/2
Add 1 to both sides:
x^2 + 2 x + 1 = 49/2
Write the left hand side as a square:
(x + 1)^2 = 49/2
Take the square root of both sides:
x + 1 = 7/sqrt(2) or x + 1 = -7/sqrt(2)
Subtract 1 from both sides:
x = 7/sqrt(2) - 1 or x + 1 = -7/sqrt(2)
Subtract 1 from both sides:
Answer: |x = 7/sqrt(2) - 1=3.950 or x = -1 - 7/sqrt(2)