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Simplifying 2x^{2}+ -5x + -5 = 0 Reorder the terms: -5 + -5x + 2x^{2}= 0 Solving -5 + -5x + 2x^{2}= 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'. -2.5 + -2.5x + x^{2}= 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.5x + 2.5 + x^{2}= 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.5x + x^{2}= 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.5x + x^{2}= 0 + 2.5 -2.5x + x^{2}= 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.5x + x^{2}= 2.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x^{2}= 2.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x^{2}= 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + -2.5x + x^{2}= 4.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -1.25) equal to 2.015564437 and -2.015564437.## Subproblem 1

x + -1.25 = 2.015564437 Simplifying x + -1.25 = 2.015564437 Reorder the terms: -1.25 + x = 2.015564437 Solving -1.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.015564437 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.015564437 + 1.25 x = 2.015564437 + 1.25 Combine like terms: 2.015564437 + 1.25 = 3.265564437 x = 3.265564437 Simplifying x = 3.265564437## Subproblem 2

x + -1.25 = -2.015564437 Simplifying x + -1.25 = -2.015564437 Reorder the terms: -1.25 + x = -2.015564437 Solving -1.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.015564437 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.015564437 + 1.25 x = -2.015564437 + 1.25 Combine like terms: -2.015564437 + 1.25 = -0.765564437 x = -0.765564437 Simplifying x = -0.765564437## Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.265564437, -0.765564437}

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