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Simplifying -110 = x2 + -32x Reorder the terms: -110 = -32x + x2 Solving -110 = -32x + x2 Solving for variable 'x'. Reorder the terms: -110 + 32x + -1x2 = -32x + 32x + x2 + -1x2 Combine like terms: -32x + 32x = 0 -110 + 32x + -1x2 = 0 + x2 + -1x2 -110 + 32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -110 + 32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 110 + -32x + x2 = 0 Move the constant term to the right: Add '-110' to each side of the equation. 110 + -32x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + -32x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -32x + x2 = 0 + -110 -32x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -32x + x2 = -110 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 = -110 + 256 Reorder the terms: 256 + -32x + x2 = -110 + 256 Combine like terms: -110 + 256 = 146 256 + -32x + x2 = 146 Factor a perfect square on the left side: (x + -16)(x + -16) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + -16) equal to 12.083045974 and -12.083045974.Subproblem 1
x + -16 = 12.083045974 Simplifying x + -16 = 12.083045974 Reorder the terms: -16 + x = 12.083045974 Solving -16 + x = 12.083045974 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 = 12.083045974 + 16 Combine like terms: -16 + 16 = 0 0 + x = 12.083045974 + 16 x = 12.083045974 + 16 Combine like terms: 12.083045974 + 16 = 28.083045974 x = 28.083045974 Simplifying x = 28.083045974Subproblem 2
x + -16 = -12.083045974 Simplifying x + -16 = -12.083045974 Reorder the terms: -16 + x = -12.083045974 Solving -16 + x = -12.083045974 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 = -12.083045974 + 16 Combine like terms: -16 + 16 = 0 0 + x = -12.083045974 + 16 x = -12.083045974 + 16 Combine like terms: -12.083045974 + 16 = 3.916954026 x = 3.916954026 Simplifying x = 3.916954026Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.083045974, 3.916954026}
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