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Simplifying x2 + 8x + 8x + 64 = 185 Reorder the terms: 64 + 8x + 8x + x2 = 185 Combine like terms: 8x + 8x = 16x 64 + 16x + x2 = 185 Solving 64 + 16x + x2 = 185 Solving for variable 'x'. Reorder the terms: 64 + -185 + 16x + x2 = 185 + -185 Combine like terms: 64 + -185 = -121 -121 + 16x + x2 = 185 + -185 Combine like terms: 185 + -185 = 0 -121 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 16x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 16x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 16x + x2 = 0 + 121 16x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 16x + x2 = 121 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 121 + 64 Reorder the terms: 64 + 16x + x2 = 121 + 64 Combine like terms: 121 + 64 = 185 64 + 16x + x2 = 185 Factor a perfect square on the left side: (x + 8)(x + 8) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + 8) equal to 13.601470509 and -13.601470509.Subproblem 1
x + 8 = 13.601470509 Simplifying x + 8 = 13.601470509 Reorder the terms: 8 + x = 13.601470509 Solving 8 + x = 13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 13.601470509 + -8 Combine like terms: 8 + -8 = 0 0 + x = 13.601470509 + -8 x = 13.601470509 + -8 Combine like terms: 13.601470509 + -8 = 5.601470509 x = 5.601470509 Simplifying x = 5.601470509Subproblem 2
x + 8 = -13.601470509 Simplifying x + 8 = -13.601470509 Reorder the terms: 8 + x = -13.601470509 Solving 8 + x = -13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -13.601470509 + -8 Combine like terms: 8 + -8 = 0 0 + x = -13.601470509 + -8 x = -13.601470509 + -8 Combine like terms: -13.601470509 + -8 = -21.601470509 x = -21.601470509 Simplifying x = -21.601470509Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.601470509, -21.601470509}
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