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Simplifying x2 + -32x + -100 = 0 Reorder the terms: -100 + -32x + x2 = 0 Solving -100 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -32x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -32x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -32x + x2 = 0 + 100 -32x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -32x + x2 = 100 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 = 100 + 256 Reorder the terms: 256 + -32x + x2 = 100 + 256 Combine like terms: 100 + 256 = 356 256 + -32x + x2 = 356 Factor a perfect square on the left side: (x + -16)(x + -16) = 356 Calculate the square root of the right side: 18.867962264 Break this problem into two subproblems by setting (x + -16) equal to 18.867962264 and -18.867962264.Subproblem 1
x + -16 = 18.867962264 Simplifying x + -16 = 18.867962264 Reorder the terms: -16 + x = 18.867962264 Solving -16 + x = 18.867962264 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 = 18.867962264 + 16 Combine like terms: -16 + 16 = 0 0 + x = 18.867962264 + 16 x = 18.867962264 + 16 Combine like terms: 18.867962264 + 16 = 34.867962264 x = 34.867962264 Simplifying x = 34.867962264Subproblem 2
x + -16 = -18.867962264 Simplifying x + -16 = -18.867962264 Reorder the terms: -16 + x = -18.867962264 Solving -16 + x = -18.867962264 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 = -18.867962264 + 16 Combine like terms: -16 + 16 = 0 0 + x = -18.867962264 + 16 x = -18.867962264 + 16 Combine like terms: -18.867962264 + 16 = -2.867962264 x = -2.867962264 Simplifying x = -2.867962264Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.867962264, -2.867962264}
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