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Simplifying x2 + 57x + -87 = 0 Reorder the terms: -87 + 57x + x2 = 0 Solving -87 + 57x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 57x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 57x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 57x + x2 = 0 + 87 57x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 57x + x2 = 87 The x term is 57x. Take half its coefficient (28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. 57x + 812.25 + x2 = 87 + 812.25 Reorder the terms: 812.25 + 57x + x2 = 87 + 812.25 Combine like terms: 87 + 812.25 = 899.25 812.25 + 57x + x2 = 899.25 Factor a perfect square on the left side: (x + 28.5)(x + 28.5) = 899.25 Calculate the square root of the right side: 29.987497395 Break this problem into two subproblems by setting (x + 28.5) equal to 29.987497395 and -29.987497395.Subproblem 1
x + 28.5 = 29.987497395 Simplifying x + 28.5 = 29.987497395 Reorder the terms: 28.5 + x = 29.987497395 Solving 28.5 + x = 29.987497395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + x = 29.987497395 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + x = 29.987497395 + -28.5 x = 29.987497395 + -28.5 Combine like terms: 29.987497395 + -28.5 = 1.487497395 x = 1.487497395 Simplifying x = 1.487497395Subproblem 2
x + 28.5 = -29.987497395 Simplifying x + 28.5 = -29.987497395 Reorder the terms: 28.5 + x = -29.987497395 Solving 28.5 + x = -29.987497395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + x = -29.987497395 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + x = -29.987497395 + -28.5 x = -29.987497395 + -28.5 Combine like terms: -29.987497395 + -28.5 = -58.487497395 x = -58.487497395 Simplifying x = -58.487497395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.487497395, -58.487497395}
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