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Simplifying x2 + -19x + -102 = 0 Reorder the terms: -102 + -19x + x2 = 0 Solving -102 + -19x + 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 + -19x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + -19x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -19x + x2 = 0 + 102 -19x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 -19x + x2 = 102 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 102 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 102 + 90.25 Combine like terms: 102 + 90.25 = 192.25 90.25 + -19x + x2 = 192.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + -9.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + -9.5 = 13.865424624 Simplifying x + -9.5 = 13.865424624 Reorder the terms: -9.5 + x = 13.865424624 Solving -9.5 + x = 13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 13.865424624 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 13.865424624 + 9.5 x = 13.865424624 + 9.5 Combine like terms: 13.865424624 + 9.5 = 23.365424624 x = 23.365424624 Simplifying x = 23.365424624Subproblem 2
x + -9.5 = -13.865424624 Simplifying x + -9.5 = -13.865424624 Reorder the terms: -9.5 + x = -13.865424624 Solving -9.5 + x = -13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -13.865424624 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -13.865424624 + 9.5 x = -13.865424624 + 9.5 Combine like terms: -13.865424624 + 9.5 = -4.365424624 x = -4.365424624 Simplifying x = -4.365424624Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.365424624, -4.365424624}
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