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Simplifying x2 + 15x + -200 = 0 Reorder the terms: -200 + 15x + x2 = 0 Solving -200 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 15x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 15x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 15x + x2 = 0 + 200 15x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 15x + x2 = 200 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 = 200 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 200 + 56.25 Combine like terms: 200 + 56.25 = 256.25 56.25 + 15x + x2 = 256.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + 7.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + 7.5 = 16.007810594 Simplifying x + 7.5 = 16.007810594 Reorder the terms: 7.5 + x = 16.007810594 Solving 7.5 + x = 16.007810594 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 = 16.007810594 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 16.007810594 + -7.5 x = 16.007810594 + -7.5 Combine like terms: 16.007810594 + -7.5 = 8.507810594 x = 8.507810594 Simplifying x = 8.507810594Subproblem 2
x + 7.5 = -16.007810594 Simplifying x + 7.5 = -16.007810594 Reorder the terms: 7.5 + x = -16.007810594 Solving 7.5 + x = -16.007810594 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 = -16.007810594 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -16.007810594 + -7.5 x = -16.007810594 + -7.5 Combine like terms: -16.007810594 + -7.5 = -23.507810594 x = -23.507810594 Simplifying x = -23.507810594Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.507810594, -23.507810594}
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