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Simplifying x2 + -16x + 64 = 54 Reorder the terms: 64 + -16x + x2 = 54 Solving 64 + -16x + x2 = 54 Solving for variable 'x'. Reorder the terms: 64 + -54 + -16x + x2 = 54 + -54 Combine like terms: 64 + -54 = 10 10 + -16x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 10 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -16x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -16x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -16x + x2 = 0 + -10 -16x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -16x + x2 = -10 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 = -10 + 64 Reorder the terms: 64 + -16x + x2 = -10 + 64 Combine like terms: -10 + 64 = 54 64 + -16x + x2 = 54 Factor a perfect square on the left side: (x + -8)(x + -8) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -8) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -8 = 7.348469228 Simplifying x + -8 = 7.348469228 Reorder the terms: -8 + x = 7.348469228 Solving -8 + x = 7.348469228 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 = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.348469228 + 8 x = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 x = 15.348469228 Simplifying x = 15.348469228Subproblem 2
x + -8 = -7.348469228 Simplifying x + -8 = -7.348469228 Reorder the terms: -8 + x = -7.348469228 Solving -8 + x = -7.348469228 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 = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.348469228 + 8 x = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 x = 0.651530772 Simplifying x = 0.651530772Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.348469228, 0.651530772}
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