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Simplifying 2x2 + -11x + -65 = 0 Reorder the terms: -65 + -11x + 2x2 = 0 Solving -65 + -11x + 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'. -32.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + -5.5x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + -5.5x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + -5.5x + x2 = 0 + 32.5 -5.5x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 -5.5x + x2 = 32.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 32.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 32.5 + 7.5625 Combine like terms: 32.5 + 7.5625 = 40.0625 7.5625 + -5.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + -2.75) equal to 6.329494451 and -6.329494451.Subproblem 1
x + -2.75 = 6.329494451 Simplifying x + -2.75 = 6.329494451 Reorder the terms: -2.75 + x = 6.329494451 Solving -2.75 + x = 6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 6.329494451 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 6.329494451 + 2.75 x = 6.329494451 + 2.75 Combine like terms: 6.329494451 + 2.75 = 9.079494451 x = 9.079494451 Simplifying x = 9.079494451Subproblem 2
x + -2.75 = -6.329494451 Simplifying x + -2.75 = -6.329494451 Reorder the terms: -2.75 + x = -6.329494451 Solving -2.75 + x = -6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -6.329494451 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -6.329494451 + 2.75 x = -6.329494451 + 2.75 Combine like terms: -6.329494451 + 2.75 = -3.579494451 x = -3.579494451 Simplifying x = -3.579494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.079494451, -3.579494451}
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