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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 = 32.231109974 X = 32.231109974 Simplifying X = 32.231109974Subproblem 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 = -37.231109974 X = -37.231109974 Simplifying X = -37.231109974Solution
The solution to the problem is based on the solutions from the subproblems. X = {32.231109974, -37.231109974}
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