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Simplifying 2x2 + -6x + -105 = 0 Reorder the terms: -105 + -6x + 2x2 = 0 Solving -105 + -6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -52.5 + -3x + x2 = 0 Move the constant term to the right: Add '52.5' to each side of the equation. -52.5 + -3x + 52.5 + x2 = 0 + 52.5 Reorder the terms: -52.5 + 52.5 + -3x + x2 = 0 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + -3x + x2 = 0 + 52.5 -3x + x2 = 0 + 52.5 Combine like terms: 0 + 52.5 = 52.5 -3x + x2 = 52.5 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 = 52.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 52.5 + 2.25 Combine like terms: 52.5 + 2.25 = 54.75 2.25 + -3x + x2 = 54.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 54.75 Calculate the square root of the right side: 7.399324293 Break this problem into two subproblems by setting (x + -1.5) equal to 7.399324293 and -7.399324293.Subproblem 1
x + -1.5 = 7.399324293 Simplifying x + -1.5 = 7.399324293 Reorder the terms: -1.5 + x = 7.399324293 Solving -1.5 + x = 7.399324293 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 = 7.399324293 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.399324293 + 1.5 x = 7.399324293 + 1.5 Combine like terms: 7.399324293 + 1.5 = 8.899324293 x = 8.899324293 Simplifying x = 8.899324293Subproblem 2
x + -1.5 = -7.399324293 Simplifying x + -1.5 = -7.399324293 Reorder the terms: -1.5 + x = -7.399324293 Solving -1.5 + x = -7.399324293 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 = -7.399324293 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.399324293 + 1.5 x = -7.399324293 + 1.5 Combine like terms: -7.399324293 + 1.5 = -5.899324293 x = -5.899324293 Simplifying x = -5.899324293Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.899324293, -5.899324293}
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