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Simplifying (x + -5)(x + 16) = 12 Reorder the terms: (-5 + x)(x + 16) = 12 Reorder the terms: (-5 + x)(16 + x) = 12 Multiply (-5 + x) * (16 + x) (-5(16 + x) + x(16 + x)) = 12 ((16 * -5 + x * -5) + x(16 + x)) = 12 ((-80 + -5x) + x(16 + x)) = 12 (-80 + -5x + (16 * x + x * x)) = 12 (-80 + -5x + (16x + x2)) = 12 Combine like terms: -5x + 16x = 11x (-80 + 11x + x2) = 12 Solving -80 + 11x + x2 = 12 Solving for variable 'x'. Reorder the terms: -80 + -12 + 11x + x2 = 12 + -12 Combine like terms: -80 + -12 = -92 -92 + 11x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -92 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 11x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 11x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 11x + x2 = 0 + 92 11x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 11x + x2 = 92 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 92 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 92 + 30.25 Combine like terms: 92 + 30.25 = 122.25 30.25 + 11x + x2 = 122.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + 5.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + 5.5 = 11.056672194 Simplifying x + 5.5 = 11.056672194 Reorder the terms: 5.5 + x = 11.056672194 Solving 5.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 11.056672194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.056672194 + -5.5 x = 11.056672194 + -5.5 Combine like terms: 11.056672194 + -5.5 = 5.556672194 x = 5.556672194 Simplifying x = 5.556672194Subproblem 2
x + 5.5 = -11.056672194 Simplifying x + 5.5 = -11.056672194 Reorder the terms: 5.5 + x = -11.056672194 Solving 5.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -11.056672194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.056672194 + -5.5 x = -11.056672194 + -5.5 Combine like terms: -11.056672194 + -5.5 = -16.556672194 x = -16.556672194 Simplifying x = -16.556672194Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.556672194, -16.556672194}
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