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Simplifying x2 + -32x + 56 = 0 Reorder the terms: 56 + -32x + x2 = 0 Solving 56 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -32x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -32x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -32x + x2 = 0 + -56 -32x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -32x + x2 = -56 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 = -56 + 256 Reorder the terms: 256 + -32x + x2 = -56 + 256 Combine like terms: -56 + 256 = 200 256 + -32x + x2 = 200 Factor a perfect square on the left side: (x + -16)(x + -16) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -16) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -16 = 14.142135624 Simplifying x + -16 = 14.142135624 Reorder the terms: -16 + x = 14.142135624 Solving -16 + x = 14.142135624 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 = 14.142135624 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.142135624 + 16 x = 14.142135624 + 16 Combine like terms: 14.142135624 + 16 = 30.142135624 x = 30.142135624 Simplifying x = 30.142135624Subproblem 2
x + -16 = -14.142135624 Simplifying x + -16 = -14.142135624 Reorder the terms: -16 + x = -14.142135624 Solving -16 + x = -14.142135624 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 = -14.142135624 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.142135624 + 16 x = -14.142135624 + 16 Combine like terms: -14.142135624 + 16 = 1.857864376 x = 1.857864376 Simplifying x = 1.857864376Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.142135624, 1.857864376}
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