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Simplifying x2 + 15x + -95.85 = 0 Reorder the terms: -95.85 + 15x + x2 = 0 Solving -95.85 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '95.85' to each side of the equation. -95.85 + 15x + 95.85 + x2 = 0 + 95.85 Reorder the terms: -95.85 + 95.85 + 15x + x2 = 0 + 95.85 Combine like terms: -95.85 + 95.85 = 0.00 0.00 + 15x + x2 = 0 + 95.85 15x + x2 = 0 + 95.85 Combine like terms: 0 + 95.85 = 95.85 15x + x2 = 95.85 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 = 95.85 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 95.85 + 56.25 Combine like terms: 95.85 + 56.25 = 152.1 56.25 + 15x + x2 = 152.1 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 152.1 Calculate the square root of the right side: 12.332882875 Break this problem into two subproblems by setting (x + 7.5) equal to 12.332882875 and -12.332882875.Subproblem 1
x + 7.5 = 12.332882875 Simplifying x + 7.5 = 12.332882875 Reorder the terms: 7.5 + x = 12.332882875 Solving 7.5 + x = 12.332882875 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 = 12.332882875 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 12.332882875 + -7.5 x = 12.332882875 + -7.5 Combine like terms: 12.332882875 + -7.5 = 4.832882875 x = 4.832882875 Simplifying x = 4.832882875Subproblem 2
x + 7.5 = -12.332882875 Simplifying x + 7.5 = -12.332882875 Reorder the terms: 7.5 + x = -12.332882875 Solving 7.5 + x = -12.332882875 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 = -12.332882875 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -12.332882875 + -7.5 x = -12.332882875 + -7.5 Combine like terms: -12.332882875 + -7.5 = -19.832882875 x = -19.832882875 Simplifying x = -19.832882875Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.832882875, -19.832882875}
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