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Simplifying 25x2 + -128x + -112 = 0 Reorder the terms: -112 + -128x + 25x2 = 0 Solving -112 + -128x + 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'. -4.48 + -5.12x + x2 = 0 Move the constant term to the right: Add '4.48' to each side of the equation. -4.48 + -5.12x + 4.48 + x2 = 0 + 4.48 Reorder the terms: -4.48 + 4.48 + -5.12x + x2 = 0 + 4.48 Combine like terms: -4.48 + 4.48 = 0.00 0.00 + -5.12x + x2 = 0 + 4.48 -5.12x + x2 = 0 + 4.48 Combine like terms: 0 + 4.48 = 4.48 -5.12x + x2 = 4.48 The x term is -5.12x. Take half its coefficient (-2.56). Square it (6.5536) and add it to both sides. Add '6.5536' to each side of the equation. -5.12x + 6.5536 + x2 = 4.48 + 6.5536 Reorder the terms: 6.5536 + -5.12x + x2 = 4.48 + 6.5536 Combine like terms: 4.48 + 6.5536 = 11.0336 6.5536 + -5.12x + x2 = 11.0336 Factor a perfect square on the left side: (x + -2.56)(x + -2.56) = 11.0336 Calculate the square root of the right side: 3.321686319 Break this problem into two subproblems by setting (x + -2.56) equal to 3.321686319 and -3.321686319.Subproblem 1
x + -2.56 = 3.321686319 Simplifying x + -2.56 = 3.321686319 Reorder the terms: -2.56 + x = 3.321686319 Solving -2.56 + x = 3.321686319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.56' to each side of the equation. -2.56 + 2.56 + x = 3.321686319 + 2.56 Combine like terms: -2.56 + 2.56 = 0.00 0.00 + x = 3.321686319 + 2.56 x = 3.321686319 + 2.56 Combine like terms: 3.321686319 + 2.56 = 5.881686319 x = 5.881686319 Simplifying x = 5.881686319Subproblem 2
x + -2.56 = -3.321686319 Simplifying x + -2.56 = -3.321686319 Reorder the terms: -2.56 + x = -3.321686319 Solving -2.56 + x = -3.321686319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.56' to each side of the equation. -2.56 + 2.56 + x = -3.321686319 + 2.56 Combine like terms: -2.56 + 2.56 = 0.00 0.00 + x = -3.321686319 + 2.56 x = -3.321686319 + 2.56 Combine like terms: -3.321686319 + 2.56 = -0.761686319 x = -0.761686319 Simplifying x = -0.761686319Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.881686319, -0.761686319}
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