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Simplifying x2 + 15x + -18000 = 0 Reorder the terms: -18000 + 15x + x2 = 0 Solving -18000 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18000' to each side of the equation. -18000 + 15x + 18000 + x2 = 0 + 18000 Reorder the terms: -18000 + 18000 + 15x + x2 = 0 + 18000 Combine like terms: -18000 + 18000 = 0 0 + 15x + x2 = 0 + 18000 15x + x2 = 0 + 18000 Combine like terms: 0 + 18000 = 18000 15x + x2 = 18000 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 = 18000 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 18000 + 56.25 Combine like terms: 18000 + 56.25 = 18056.25 56.25 + 15x + x2 = 18056.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 18056.25 Calculate the square root of the right side: 134.373546504 Break this problem into two subproblems by setting (x + 7.5) equal to 134.373546504 and -134.373546504.Subproblem 1
x + 7.5 = 134.373546504 Simplifying x + 7.5 = 134.373546504 Reorder the terms: 7.5 + x = 134.373546504 Solving 7.5 + x = 134.373546504 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 = 134.373546504 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 134.373546504 + -7.5 x = 134.373546504 + -7.5 Combine like terms: 134.373546504 + -7.5 = 126.873546504 x = 126.873546504 Simplifying x = 126.873546504Subproblem 2
x + 7.5 = -134.373546504 Simplifying x + 7.5 = -134.373546504 Reorder the terms: 7.5 + x = -134.373546504 Solving 7.5 + x = -134.373546504 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 = -134.373546504 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -134.373546504 + -7.5 x = -134.373546504 + -7.5 Combine like terms: -134.373546504 + -7.5 = -141.873546504 x = -141.873546504 Simplifying x = -141.873546504Solution
The solution to the problem is based on the solutions from the subproblems. x = {126.873546504, -141.873546504}
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