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Simplifying x2 + 68x + 15 = 0 Reorder the terms: 15 + 68x + x2 = 0 Solving 15 + 68x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 68x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 68x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 68x + x2 = 0 + -15 68x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 68x + x2 = -15 The x term is 68x. Take half its coefficient (34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. 68x + 1156 + x2 = -15 + 1156 Reorder the terms: 1156 + 68x + x2 = -15 + 1156 Combine like terms: -15 + 1156 = 1141 1156 + 68x + x2 = 1141 Factor a perfect square on the left side: (x + 34)(x + 34) = 1141 Calculate the square root of the right side: 33.778691508 Break this problem into two subproblems by setting (x + 34) equal to 33.778691508 and -33.778691508.Subproblem 1
x + 34 = 33.778691508 Simplifying x + 34 = 33.778691508 Reorder the terms: 34 + x = 33.778691508 Solving 34 + x = 33.778691508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = 33.778691508 + -34 Combine like terms: 34 + -34 = 0 0 + x = 33.778691508 + -34 x = 33.778691508 + -34 Combine like terms: 33.778691508 + -34 = -0.221308492 x = -0.221308492 Simplifying x = -0.221308492Subproblem 2
x + 34 = -33.778691508 Simplifying x + 34 = -33.778691508 Reorder the terms: 34 + x = -33.778691508 Solving 34 + x = -33.778691508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = -33.778691508 + -34 Combine like terms: 34 + -34 = 0 0 + x = -33.778691508 + -34 x = -33.778691508 + -34 Combine like terms: -33.778691508 + -34 = -67.778691508 x = -67.778691508 Simplifying x = -67.778691508Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.221308492, -67.778691508}
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