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Simplifying 27x2 + -15x + -160 = 0 Reorder the terms: -160 + -15x + 27x2 = 0 Solving -160 + -15x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -5.925925926 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '5.925925926' to each side of the equation. -5.925925926 + -0.5555555556x + 5.925925926 + x2 = 0 + 5.925925926 Reorder the terms: -5.925925926 + 5.925925926 + -0.5555555556x + x2 = 0 + 5.925925926 Combine like terms: -5.925925926 + 5.925925926 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 5.925925926 -0.5555555556x + x2 = 0 + 5.925925926 Combine like terms: 0 + 5.925925926 = 5.925925926 -0.5555555556x + x2 = 5.925925926 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 5.925925926 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 5.925925926 + 0.07716049384 Combine like terms: 5.925925926 + 0.07716049384 = 6.00308641984 0.07716049384 + -0.5555555556x + x2 = 6.00308641984 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 6.00308641984 Calculate the square root of the right side: 2.450119675 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 2.450119675 and -2.450119675.Subproblem 1
x + -0.2777777778 = 2.450119675 Simplifying x + -0.2777777778 = 2.450119675 Reorder the terms: -0.2777777778 + x = 2.450119675 Solving -0.2777777778 + x = 2.450119675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 2.450119675 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 2.450119675 + 0.2777777778 x = 2.450119675 + 0.2777777778 Combine like terms: 2.450119675 + 0.2777777778 = 2.7278974528 x = 2.7278974528 Simplifying x = 2.7278974528Subproblem 2
x + -0.2777777778 = -2.450119675 Simplifying x + -0.2777777778 = -2.450119675 Reorder the terms: -0.2777777778 + x = -2.450119675 Solving -0.2777777778 + x = -2.450119675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -2.450119675 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -2.450119675 + 0.2777777778 x = -2.450119675 + 0.2777777778 Combine like terms: -2.450119675 + 0.2777777778 = -2.1723418972 x = -2.1723418972 Simplifying x = -2.1723418972Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7278974528, -2.1723418972}
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