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Simplifying 25x2 + -12x + -128 = 0 Reorder the terms: -128 + -12x + 25x2 = 0 Solving -128 + -12x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -5.12 + -0.48x + x2 = 0 Move the constant term to the right: Add '5.12' to each side of the equation. -5.12 + -0.48x + 5.12 + x2 = 0 + 5.12 Reorder the terms: -5.12 + 5.12 + -0.48x + x2 = 0 + 5.12 Combine like terms: -5.12 + 5.12 = 0.00 0.00 + -0.48x + x2 = 0 + 5.12 -0.48x + x2 = 0 + 5.12 Combine like terms: 0 + 5.12 = 5.12 -0.48x + x2 = 5.12 The x term is -0.48x. Take half its coefficient (-0.24). Square it (0.0576) and add it to both sides. Add '0.0576' to each side of the equation. -0.48x + 0.0576 + x2 = 5.12 + 0.0576 Reorder the terms: 0.0576 + -0.48x + x2 = 5.12 + 0.0576 Combine like terms: 5.12 + 0.0576 = 5.1776 0.0576 + -0.48x + x2 = 5.1776 Factor a perfect square on the left side: (x + -0.24)(x + -0.24) = 5.1776 Calculate the square root of the right side: 2.275434025 Break this problem into two subproblems by setting (x + -0.24) equal to 2.275434025 and -2.275434025.Subproblem 1
x + -0.24 = 2.275434025 Simplifying x + -0.24 = 2.275434025 Reorder the terms: -0.24 + x = 2.275434025 Solving -0.24 + x = 2.275434025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = 2.275434025 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = 2.275434025 + 0.24 x = 2.275434025 + 0.24 Combine like terms: 2.275434025 + 0.24 = 2.515434025 x = 2.515434025 Simplifying x = 2.515434025Subproblem 2
x + -0.24 = -2.275434025 Simplifying x + -0.24 = -2.275434025 Reorder the terms: -0.24 + x = -2.275434025 Solving -0.24 + x = -2.275434025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = -2.275434025 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = -2.275434025 + 0.24 x = -2.275434025 + 0.24 Combine like terms: -2.275434025 + 0.24 = -2.035434025 x = -2.035434025 Simplifying x = -2.035434025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.515434025, -2.035434025}
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