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Simplifying x2 + -3x + -106 = 0 Reorder the terms: -106 + -3x + x2 = 0 Solving -106 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + -3x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + -3x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + -3x + x2 = 0 + 106 -3x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 -3x + x2 = 106 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 106 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 106 + 2.25 Combine like terms: 106 + 2.25 = 108.25 2.25 + -3x + x2 = 108.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + -1.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + -1.5 = 10.404326023 Simplifying x + -1.5 = 10.404326023 Reorder the terms: -1.5 + x = 10.404326023 Solving -1.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 10.404326023 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.404326023 + 1.5 x = 10.404326023 + 1.5 Combine like terms: 10.404326023 + 1.5 = 11.904326023 x = 11.904326023 Simplifying x = 11.904326023Subproblem 2
x + -1.5 = -10.404326023 Simplifying x + -1.5 = -10.404326023 Reorder the terms: -1.5 + x = -10.404326023 Solving -1.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -10.404326023 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.404326023 + 1.5 x = -10.404326023 + 1.5 Combine like terms: -10.404326023 + 1.5 = -8.904326023 x = -8.904326023 Simplifying x = -8.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.904326023, -8.904326023}
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