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Simplifying x2 + -68x + -102 = 0 Reorder the terms: -102 + -68x + x2 = 0 Solving -102 + -68x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + -68x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + -68x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -68x + x2 = 0 + 102 -68x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 -68x + x2 = 102 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 = 102 + 1156 Reorder the terms: 1156 + -68x + x2 = 102 + 1156 Combine like terms: 102 + 1156 = 1258 1156 + -68x + x2 = 1258 Factor a perfect square on the left side: (x + -34)(x + -34) = 1258 Calculate the square root of the right side: 35.468295702 Break this problem into two subproblems by setting (x + -34) equal to 35.468295702 and -35.468295702.Subproblem 1
x + -34 = 35.468295702 Simplifying x + -34 = 35.468295702 Reorder the terms: -34 + x = 35.468295702 Solving -34 + x = 35.468295702 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 = 35.468295702 + 34 Combine like terms: -34 + 34 = 0 0 + x = 35.468295702 + 34 x = 35.468295702 + 34 Combine like terms: 35.468295702 + 34 = 69.468295702 x = 69.468295702 Simplifying x = 69.468295702Subproblem 2
x + -34 = -35.468295702 Simplifying x + -34 = -35.468295702 Reorder the terms: -34 + x = -35.468295702 Solving -34 + x = -35.468295702 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 = -35.468295702 + 34 Combine like terms: -34 + 34 = 0 0 + x = -35.468295702 + 34 x = -35.468295702 + 34 Combine like terms: -35.468295702 + 34 = -1.468295702 x = -1.468295702 Simplifying x = -1.468295702Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.468295702, -1.468295702}
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