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Simplifying -25y2 + -128y + 112 = 0 Reorder the terms: 112 + -128y + -25y2 = 0 Solving 112 + -128y + -25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -4.48 + 5.12y + y2 = 0 Move the constant term to the right: Add '4.48' to each side of the equation. -4.48 + 5.12y + 4.48 + y2 = 0 + 4.48 Reorder the terms: -4.48 + 4.48 + 5.12y + y2 = 0 + 4.48 Combine like terms: -4.48 + 4.48 = 0.00 0.00 + 5.12y + y2 = 0 + 4.48 5.12y + y2 = 0 + 4.48 Combine like terms: 0 + 4.48 = 4.48 5.12y + y2 = 4.48 The y term is 5.12y. 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. 5.12y + 6.5536 + y2 = 4.48 + 6.5536 Reorder the terms: 6.5536 + 5.12y + y2 = 4.48 + 6.5536 Combine like terms: 4.48 + 6.5536 = 11.0336 6.5536 + 5.12y + y2 = 11.0336 Factor a perfect square on the left side: (y + 2.56)(y + 2.56) = 11.0336 Calculate the square root of the right side: 3.321686319 Break this problem into two subproblems by setting (y + 2.56) equal to 3.321686319 and -3.321686319.Subproblem 1
y + 2.56 = 3.321686319 Simplifying y + 2.56 = 3.321686319 Reorder the terms: 2.56 + y = 3.321686319 Solving 2.56 + y = 3.321686319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.56' to each side of the equation. 2.56 + -2.56 + y = 3.321686319 + -2.56 Combine like terms: 2.56 + -2.56 = 0.00 0.00 + y = 3.321686319 + -2.56 y = 3.321686319 + -2.56 Combine like terms: 3.321686319 + -2.56 = 0.761686319 y = 0.761686319 Simplifying y = 0.761686319Subproblem 2
y + 2.56 = -3.321686319 Simplifying y + 2.56 = -3.321686319 Reorder the terms: 2.56 + y = -3.321686319 Solving 2.56 + y = -3.321686319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.56' to each side of the equation. 2.56 + -2.56 + y = -3.321686319 + -2.56 Combine like terms: 2.56 + -2.56 = 0.00 0.00 + y = -3.321686319 + -2.56 y = -3.321686319 + -2.56 Combine like terms: -3.321686319 + -2.56 = -5.881686319 y = -5.881686319 Simplifying y = -5.881686319Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.761686319, -5.881686319}
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