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Simplifying 65x2 + -96x + 27 = 0 Reorder the terms: 27 + -96x + 65x2 = 0 Solving 27 + -96x + 65x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. 0.4153846154 + -1.476923077x + x2 = 0 Move the constant term to the right: Add '-0.4153846154' to each side of the equation. 0.4153846154 + -1.476923077x + -0.4153846154 + x2 = 0 + -0.4153846154 Reorder the terms: 0.4153846154 + -0.4153846154 + -1.476923077x + x2 = 0 + -0.4153846154 Combine like terms: 0.4153846154 + -0.4153846154 = 0.0000000000 0.0000000000 + -1.476923077x + x2 = 0 + -0.4153846154 -1.476923077x + x2 = 0 + -0.4153846154 Combine like terms: 0 + -0.4153846154 = -0.4153846154 -1.476923077x + x2 = -0.4153846154 The x term is -1.476923077x. Take half its coefficient (-0.7384615385). Square it (0.5453254438) and add it to both sides. Add '0.5453254438' to each side of the equation. -1.476923077x + 0.5453254438 + x2 = -0.4153846154 + 0.5453254438 Reorder the terms: 0.5453254438 + -1.476923077x + x2 = -0.4153846154 + 0.5453254438 Combine like terms: -0.4153846154 + 0.5453254438 = 0.1299408284 0.5453254438 + -1.476923077x + x2 = 0.1299408284 Factor a perfect square on the left side: (x + -0.7384615385)(x + -0.7384615385) = 0.1299408284 Calculate the square root of the right side: 0.360473062 Break this problem into two subproblems by setting (x + -0.7384615385) equal to 0.360473062 and -0.360473062.Subproblem 1
x + -0.7384615385 = 0.360473062 Simplifying x + -0.7384615385 = 0.360473062 Reorder the terms: -0.7384615385 + x = 0.360473062 Solving -0.7384615385 + x = 0.360473062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7384615385' to each side of the equation. -0.7384615385 + 0.7384615385 + x = 0.360473062 + 0.7384615385 Combine like terms: -0.7384615385 + 0.7384615385 = 0.0000000000 0.0000000000 + x = 0.360473062 + 0.7384615385 x = 0.360473062 + 0.7384615385 Combine like terms: 0.360473062 + 0.7384615385 = 1.0989346005 x = 1.0989346005 Simplifying x = 1.0989346005Subproblem 2
x + -0.7384615385 = -0.360473062 Simplifying x + -0.7384615385 = -0.360473062 Reorder the terms: -0.7384615385 + x = -0.360473062 Solving -0.7384615385 + x = -0.360473062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7384615385' to each side of the equation. -0.7384615385 + 0.7384615385 + x = -0.360473062 + 0.7384615385 Combine like terms: -0.7384615385 + 0.7384615385 = 0.0000000000 0.0000000000 + x = -0.360473062 + 0.7384615385 x = -0.360473062 + 0.7384615385 Combine like terms: -0.360473062 + 0.7384615385 = 0.3779884765 x = 0.3779884765 Simplifying x = 0.3779884765Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0989346005, 0.3779884765}
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