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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 = 320 256 + 32x + x2 = 320 Factor a perfect square on the left side: (x + 16)(x + 16) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + 16) equal to 17.88854382 and -17.88854382.Subproblem 1
x + 16 = 17.88854382 Simplifying x + 16 = 17.88854382 Reorder the terms: 16 + x = 17.88854382 Solving 16 + x = 17.88854382 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 = 17.88854382 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.88854382 + -16 x = 17.88854382 + -16 Combine like terms: 17.88854382 + -16 = 1.88854382 x = 1.88854382 Simplifying x = 1.88854382Subproblem 2
x + 16 = -17.88854382 Simplifying x + 16 = -17.88854382 Reorder the terms: 16 + x = -17.88854382 Solving 16 + x = -17.88854382 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 = -17.88854382 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.88854382 + -16 x = -17.88854382 + -16 Combine like terms: -17.88854382 + -16 = -33.88854382 x = -33.88854382 Simplifying x = -33.88854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.88854382, -33.88854382}
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