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Simplifying x2 + 1.5x + -1200 = 0 Reorder the terms: -1200 + 1.5x + x2 = 0 Solving -1200 + 1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 1.5x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 1.5x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 1.5x + x2 = 0 + 1200 1.5x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 1.5x + x2 = 1200 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1200 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1200 + 0.5625 Combine like terms: 1200 + 0.5625 = 1200.5625 0.5625 + 1.5x + x2 = 1200.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1200.5625 Calculate the square root of the right side: 34.649134188 Break this problem into two subproblems by setting (x + 0.75) equal to 34.649134188 and -34.649134188.Subproblem 1
x + 0.75 = 34.649134188 Simplifying x + 0.75 = 34.649134188 Reorder the terms: 0.75 + x = 34.649134188 Solving 0.75 + x = 34.649134188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 34.649134188 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 34.649134188 + -0.75 x = 34.649134188 + -0.75 Combine like terms: 34.649134188 + -0.75 = 33.899134188 x = 33.899134188 Simplifying x = 33.899134188Subproblem 2
x + 0.75 = -34.649134188 Simplifying x + 0.75 = -34.649134188 Reorder the terms: 0.75 + x = -34.649134188 Solving 0.75 + x = -34.649134188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -34.649134188 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -34.649134188 + -0.75 x = -34.649134188 + -0.75 Combine like terms: -34.649134188 + -0.75 = -35.399134188 x = -35.399134188 Simplifying x = -35.399134188Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.899134188, -35.399134188}
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