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Simplifying x2 + 13x + -86.75 = 0 Reorder the terms: -86.75 + 13x + x2 = 0 Solving -86.75 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86.75' to each side of the equation. -86.75 + 13x + 86.75 + x2 = 0 + 86.75 Reorder the terms: -86.75 + 86.75 + 13x + x2 = 0 + 86.75 Combine like terms: -86.75 + 86.75 = 0.00 0.00 + 13x + x2 = 0 + 86.75 13x + x2 = 0 + 86.75 Combine like terms: 0 + 86.75 = 86.75 13x + x2 = 86.75 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 86.75 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 86.75 + 42.25 Combine like terms: 86.75 + 42.25 = 129 42.25 + 13x + x2 = 129 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 6.5) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 6.5 = 11.357816692 Simplifying x + 6.5 = 11.357816692 Reorder the terms: 6.5 + x = 11.357816692 Solving 6.5 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 11.357816692 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 11.357816692 + -6.5 x = 11.357816692 + -6.5 Combine like terms: 11.357816692 + -6.5 = 4.857816692 x = 4.857816692 Simplifying x = 4.857816692Subproblem 2
x + 6.5 = -11.357816692 Simplifying x + 6.5 = -11.357816692 Reorder the terms: 6.5 + x = -11.357816692 Solving 6.5 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -11.357816692 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -11.357816692 + -6.5 x = -11.357816692 + -6.5 Combine like terms: -11.357816692 + -6.5 = -17.857816692 x = -17.857816692 Simplifying x = -17.857816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.857816692, -17.857816692}
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