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Simplifying x2 + 15x + -2250 = 0 Reorder the terms: -2250 + 15x + x2 = 0 Solving -2250 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2250' to each side of the equation. -2250 + 15x + 2250 + x2 = 0 + 2250 Reorder the terms: -2250 + 2250 + 15x + x2 = 0 + 2250 Combine like terms: -2250 + 2250 = 0 0 + 15x + x2 = 0 + 2250 15x + x2 = 0 + 2250 Combine like terms: 0 + 2250 = 2250 15x + x2 = 2250 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 = 2250 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 2250 + 56.25 Combine like terms: 2250 + 56.25 = 2306.25 56.25 + 15x + x2 = 2306.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 2306.25 Calculate the square root of the right side: 48.023431781 Break this problem into two subproblems by setting (x + 7.5) equal to 48.023431781 and -48.023431781.Subproblem 1
x + 7.5 = 48.023431781 Simplifying x + 7.5 = 48.023431781 Reorder the terms: 7.5 + x = 48.023431781 Solving 7.5 + x = 48.023431781 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 = 48.023431781 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 48.023431781 + -7.5 x = 48.023431781 + -7.5 Combine like terms: 48.023431781 + -7.5 = 40.523431781 x = 40.523431781 Simplifying x = 40.523431781Subproblem 2
x + 7.5 = -48.023431781 Simplifying x + 7.5 = -48.023431781 Reorder the terms: 7.5 + x = -48.023431781 Solving 7.5 + x = -48.023431781 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 = -48.023431781 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -48.023431781 + -7.5 x = -48.023431781 + -7.5 Combine like terms: -48.023431781 + -7.5 = -55.523431781 x = -55.523431781 Simplifying x = -55.523431781Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.523431781, -55.523431781}
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