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Simplifying x2 + -32x + 81 = 0 Reorder the terms: 81 + -32x + x2 = 0 Solving 81 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -32x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + -32x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -32x + x2 = 0 + -81 -32x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 -32x + x2 = -81 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -81 + 256 Reorder the terms: 256 + -32x + x2 = -81 + 256 Combine like terms: -81 + 256 = 175 256 + -32x + x2 = 175 Factor a perfect square on the left side: (x + -16)(x + -16) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -16) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -16 = 13.228756555 Simplifying x + -16 = 13.228756555 Reorder the terms: -16 + x = 13.228756555 Solving -16 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 13.228756555 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.228756555 + 16 x = 13.228756555 + 16 Combine like terms: 13.228756555 + 16 = 29.228756555 x = 29.228756555 Simplifying x = 29.228756555Subproblem 2
x + -16 = -13.228756555 Simplifying x + -16 = -13.228756555 Reorder the terms: -16 + x = -13.228756555 Solving -16 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -13.228756555 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.228756555 + 16 x = -13.228756555 + 16 Combine like terms: -13.228756555 + 16 = 2.771243445 x = 2.771243445 Simplifying x = 2.771243445Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.228756555, 2.771243445}
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