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Simplifying x2 + 32x + 64 = 0 Reorder the terms: 64 + 32x + x2 = 0 Solving 64 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 32x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 32x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 32x + x2 = 0 + -64 32x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 32x + x2 = -64 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 = -64 + 256 Reorder the terms: 256 + 32x + x2 = -64 + 256 Combine like terms: -64 + 256 = 192 256 + 32x + x2 = 192 Factor a perfect square on the left side: (x + 16)(x + 16) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + 16) equal to 13.856406461 and -13.856406461.Subproblem 1
x + 16 = 13.856406461 Simplifying x + 16 = 13.856406461 Reorder the terms: 16 + x = 13.856406461 Solving 16 + x = 13.856406461 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 = 13.856406461 + -16 Combine like terms: 16 + -16 = 0 0 + x = 13.856406461 + -16 x = 13.856406461 + -16 Combine like terms: 13.856406461 + -16 = -2.143593539 x = -2.143593539 Simplifying x = -2.143593539Subproblem 2
x + 16 = -13.856406461 Simplifying x + 16 = -13.856406461 Reorder the terms: 16 + x = -13.856406461 Solving 16 + x = -13.856406461 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 = -13.856406461 + -16 Combine like terms: 16 + -16 = 0 0 + x = -13.856406461 + -16 x = -13.856406461 + -16 Combine like terms: -13.856406461 + -16 = -29.856406461 x = -29.856406461 Simplifying x = -29.856406461Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.143593539, -29.856406461}
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