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Simplifying x(x + 5) = 157 Reorder the terms: x(5 + x) = 157 (5 * x + x * x) = 157 (5x + x2) = 157 Solving 5x + x2 = 157 Solving for variable 'x'. Reorder the terms: -157 + 5x + x2 = 157 + -157 Combine like terms: 157 + -157 = 0 -157 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '157' to each side of the equation. -157 + 5x + 157 + x2 = 0 + 157 Reorder the terms: -157 + 157 + 5x + x2 = 0 + 157 Combine like terms: -157 + 157 = 0 0 + 5x + x2 = 0 + 157 5x + x2 = 0 + 157 Combine like terms: 0 + 157 = 157 5x + x2 = 157 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 157 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 157 + 6.25 Combine like terms: 157 + 6.25 = 163.25 6.25 + 5x + x2 = 163.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 163.25 Calculate the square root of the right side: 12.776932339 Break this problem into two subproblems by setting (x + 2.5) equal to 12.776932339 and -12.776932339.Subproblem 1
x + 2.5 = 12.776932339 Simplifying x + 2.5 = 12.776932339 Reorder the terms: 2.5 + x = 12.776932339 Solving 2.5 + x = 12.776932339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 12.776932339 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.776932339 + -2.5 x = 12.776932339 + -2.5 Combine like terms: 12.776932339 + -2.5 = 10.276932339 x = 10.276932339 Simplifying x = 10.276932339Subproblem 2
x + 2.5 = -12.776932339 Simplifying x + 2.5 = -12.776932339 Reorder the terms: 2.5 + x = -12.776932339 Solving 2.5 + x = -12.776932339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -12.776932339 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.776932339 + -2.5 x = -12.776932339 + -2.5 Combine like terms: -12.776932339 + -2.5 = -15.276932339 x = -15.276932339 Simplifying x = -15.276932339Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.276932339, -15.276932339}
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