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Simplifying -8x2 + 15x = 88 + -9x2 Reorder the terms: 15x + -8x2 = 88 + -9x2 Solving 15x + -8x2 = 88 + -9x2 Solving for variable 'x'. Reorder the terms: -88 + 15x + -8x2 + 9x2 = 88 + -9x2 + -88 + 9x2 Combine like terms: -8x2 + 9x2 = 1x2 -88 + 15x + 1x2 = 88 + -9x2 + -88 + 9x2 Reorder the terms: -88 + 15x + 1x2 = 88 + -88 + -9x2 + 9x2 Combine like terms: 88 + -88 = 0 -88 + 15x + 1x2 = 0 + -9x2 + 9x2 -88 + 15x + 1x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -88 + 15x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 15x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 15x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 15x + x2 = 0 + 88 15x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 15x + x2 = 88 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 88 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 88 + 56.25 Combine like terms: 88 + 56.25 = 144.25 56.25 + 15x + x2 = 144.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + 7.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + 7.5 = 12.010412149 Simplifying x + 7.5 = 12.010412149 Reorder the terms: 7.5 + x = 12.010412149 Solving 7.5 + x = 12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 12.010412149 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 12.010412149 + -7.5 x = 12.010412149 + -7.5 Combine like terms: 12.010412149 + -7.5 = 4.510412149 x = 4.510412149 Simplifying x = 4.510412149Subproblem 2
x + 7.5 = -12.010412149 Simplifying x + 7.5 = -12.010412149 Reorder the terms: 7.5 + x = -12.010412149 Solving 7.5 + x = -12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -12.010412149 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -12.010412149 + -7.5 x = -12.010412149 + -7.5 Combine like terms: -12.010412149 + -7.5 = -19.510412149 x = -19.510412149 Simplifying x = -19.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.510412149, -19.510412149}
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