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Simplifying (x + 800)(x + 120) = 16500 Reorder the terms: (800 + x)(x + 120) = 16500 Reorder the terms: (800 + x)(120 + x) = 16500 Multiply (800 + x) * (120 + x) (800(120 + x) + x(120 + x)) = 16500 ((120 * 800 + x * 800) + x(120 + x)) = 16500 ((96000 + 800x) + x(120 + x)) = 16500 (96000 + 800x + (120 * x + x * x)) = 16500 (96000 + 800x + (120x + x2)) = 16500 Combine like terms: 800x + 120x = 920x (96000 + 920x + x2) = 16500 Solving 96000 + 920x + x2 = 16500 Solving for variable 'x'. Reorder the terms: 96000 + -16500 + 920x + x2 = 16500 + -16500 Combine like terms: 96000 + -16500 = 79500 79500 + 920x + x2 = 16500 + -16500 Combine like terms: 16500 + -16500 = 0 79500 + 920x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-79500' to each side of the equation. 79500 + 920x + -79500 + x2 = 0 + -79500 Reorder the terms: 79500 + -79500 + 920x + x2 = 0 + -79500 Combine like terms: 79500 + -79500 = 0 0 + 920x + x2 = 0 + -79500 920x + x2 = 0 + -79500 Combine like terms: 0 + -79500 = -79500 920x + x2 = -79500 The x term is 920x. Take half its coefficient (460). Square it (211600) and add it to both sides. Add '211600' to each side of the equation. 920x + 211600 + x2 = -79500 + 211600 Reorder the terms: 211600 + 920x + x2 = -79500 + 211600 Combine like terms: -79500 + 211600 = 132100 211600 + 920x + x2 = 132100 Factor a perfect square on the left side: (x + 460)(x + 460) = 132100 Calculate the square root of the right side: 363.455636908 Break this problem into two subproblems by setting (x + 460) equal to 363.455636908 and -363.455636908.Subproblem 1
x + 460 = 363.455636908 Simplifying x + 460 = 363.455636908 Reorder the terms: 460 + x = 363.455636908 Solving 460 + x = 363.455636908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-460' to each side of the equation. 460 + -460 + x = 363.455636908 + -460 Combine like terms: 460 + -460 = 0 0 + x = 363.455636908 + -460 x = 363.455636908 + -460 Combine like terms: 363.455636908 + -460 = -96.544363092 x = -96.544363092 Simplifying x = -96.544363092Subproblem 2
x + 460 = -363.455636908 Simplifying x + 460 = -363.455636908 Reorder the terms: 460 + x = -363.455636908 Solving 460 + x = -363.455636908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-460' to each side of the equation. 460 + -460 + x = -363.455636908 + -460 Combine like terms: 460 + -460 = 0 0 + x = -363.455636908 + -460 x = -363.455636908 + -460 Combine like terms: -363.455636908 + -460 = -823.455636908 x = -823.455636908 Simplifying x = -823.455636908Solution
The solution to the problem is based on the solutions from the subproblems. x = {-96.544363092, -823.455636908}
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