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Simplifying 2x2 + 6x + -263 = 0 Reorder the terms: -263 + 6x + 2x2 = 0 Solving -263 + 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'. -131.5 + 3x + x2 = 0 Move the constant term to the right: Add '131.5' to each side of the equation. -131.5 + 3x + 131.5 + x2 = 0 + 131.5 Reorder the terms: -131.5 + 131.5 + 3x + x2 = 0 + 131.5 Combine like terms: -131.5 + 131.5 = 0.0 0.0 + 3x + x2 = 0 + 131.5 3x + x2 = 0 + 131.5 Combine like terms: 0 + 131.5 = 131.5 3x + x2 = 131.5 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 = 131.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 131.5 + 2.25 Combine like terms: 131.5 + 2.25 = 133.75 2.25 + 3x + x2 = 133.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 133.75 Calculate the square root of the right side: 11.565033506 Break this problem into two subproblems by setting (x + 1.5) equal to 11.565033506 and -11.565033506.Subproblem 1
x + 1.5 = 11.565033506 Simplifying x + 1.5 = 11.565033506 Reorder the terms: 1.5 + x = 11.565033506 Solving 1.5 + x = 11.565033506 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 = 11.565033506 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.565033506 + -1.5 x = 11.565033506 + -1.5 Combine like terms: 11.565033506 + -1.5 = 10.065033506 x = 10.065033506 Simplifying x = 10.065033506Subproblem 2
x + 1.5 = -11.565033506 Simplifying x + 1.5 = -11.565033506 Reorder the terms: 1.5 + x = -11.565033506 Solving 1.5 + x = -11.565033506 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 = -11.565033506 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.565033506 + -1.5 x = -11.565033506 + -1.5 Combine like terms: -11.565033506 + -1.5 = -13.065033506 x = -13.065033506 Simplifying x = -13.065033506Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.065033506, -13.065033506}
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