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Simplifying 0 = 400 + -117.2x + -1x2 Solving 0 = 400 + -117.2x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + 117.2x + x2 = 400 + -117.2x + -1x2 + -400 + 117.2x + x2 Reorder the terms: -400 + 117.2x + x2 = 400 + -400 + -117.2x + 117.2x + -1x2 + x2 Combine like terms: 400 + -400 = 0 -400 + 117.2x + x2 = 0 + -117.2x + 117.2x + -1x2 + x2 -400 + 117.2x + x2 = -117.2x + 117.2x + -1x2 + x2 Combine like terms: -117.2x + 117.2x = 0.0 -400 + 117.2x + x2 = 0.0 + -1x2 + x2 -400 + 117.2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -400 + 117.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 117.2x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 117.2x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 117.2x + x2 = 0 + 400 117.2x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 117.2x + x2 = 400 The x term is 117.2x. Take half its coefficient (58.6). Square it (3433.96) and add it to both sides. Add '3433.96' to each side of the equation. 117.2x + 3433.96 + x2 = 400 + 3433.96 Reorder the terms: 3433.96 + 117.2x + x2 = 400 + 3433.96 Combine like terms: 400 + 3433.96 = 3833.96 3433.96 + 117.2x + x2 = 3833.96 Factor a perfect square on the left side: (x + 58.6)(x + 58.6) = 3833.96 Calculate the square root of the right side: 61.91897932 Break this problem into two subproblems by setting (x + 58.6) equal to 61.91897932 and -61.91897932.Subproblem 1
x + 58.6 = 61.91897932 Simplifying x + 58.6 = 61.91897932 Reorder the terms: 58.6 + x = 61.91897932 Solving 58.6 + x = 61.91897932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.6' to each side of the equation. 58.6 + -58.6 + x = 61.91897932 + -58.6 Combine like terms: 58.6 + -58.6 = 0.0 0.0 + x = 61.91897932 + -58.6 x = 61.91897932 + -58.6 Combine like terms: 61.91897932 + -58.6 = 3.31897932 x = 3.31897932 Simplifying x = 3.31897932Subproblem 2
x + 58.6 = -61.91897932 Simplifying x + 58.6 = -61.91897932 Reorder the terms: 58.6 + x = -61.91897932 Solving 58.6 + x = -61.91897932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.6' to each side of the equation. 58.6 + -58.6 + x = -61.91897932 + -58.6 Combine like terms: 58.6 + -58.6 = 0.0 0.0 + x = -61.91897932 + -58.6 x = -61.91897932 + -58.6 Combine like terms: -61.91897932 + -58.6 = -120.51897932 x = -120.51897932 Simplifying x = -120.51897932Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.31897932, -120.51897932}
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