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Simplifying x2 + -2x + -87 = 0 Reorder the terms: -87 + -2x + x2 = 0 Solving -87 + -2x + 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 + -2x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + -2x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + -2x + x2 = 0 + 87 -2x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 -2x + x2 = 87 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 87 + 1 Reorder the terms: 1 + -2x + x2 = 87 + 1 Combine like terms: 87 + 1 = 88 1 + -2x + x2 = 88 Factor a perfect square on the left side: (x + -1)(x + -1) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -1) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -1 = 9.38083152 Simplifying x + -1 = 9.38083152 Reorder the terms: -1 + x = 9.38083152 Solving -1 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.38083152 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.38083152 + 1 x = 9.38083152 + 1 Combine like terms: 9.38083152 + 1 = 10.38083152 x = 10.38083152 Simplifying x = 10.38083152Subproblem 2
x + -1 = -9.38083152 Simplifying x + -1 = -9.38083152 Reorder the terms: -1 + x = -9.38083152 Solving -1 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.38083152 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.38083152 + 1 x = -9.38083152 + 1 Combine like terms: -9.38083152 + 1 = -8.38083152 x = -8.38083152 Simplifying x = -8.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.38083152, -8.38083152}
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