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Simplifying x2 + -5x + -1200 = 0 Reorder the terms: -1200 + -5x + x2 = 0 Solving -1200 + -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 + -5x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -5x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -5x + x2 = 0 + 1200 -5x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -5x + x2 = 1200 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1200 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1200 + 6.25 Combine like terms: 1200 + 6.25 = 1206.25 6.25 + -5x + x2 = 1206.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1206.25 Calculate the square root of the right side: 34.731109974 Break this problem into two subproblems by setting (x + -2.5) equal to 34.731109974 and -34.731109974.Subproblem 1
x + -2.5 = 34.731109974 Simplifying x + -2.5 = 34.731109974 Reorder the terms: -2.5 + x = 34.731109974 Solving -2.5 + x = 34.731109974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 34.731109974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 34.731109974 + 2.5 x = 34.731109974 + 2.5 Combine like terms: 34.731109974 + 2.5 = 37.231109974 x = 37.231109974 Simplifying x = 37.231109974Subproblem 2
x + -2.5 = -34.731109974 Simplifying x + -2.5 = -34.731109974 Reorder the terms: -2.5 + x = -34.731109974 Solving -2.5 + x = -34.731109974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -34.731109974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -34.731109974 + 2.5 x = -34.731109974 + 2.5 Combine like terms: -34.731109974 + 2.5 = -32.231109974 x = -32.231109974 Simplifying x = -32.231109974Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.231109974, -32.231109974}
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