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Simplifying 2y2 + -19y = 35 Reorder the terms: -19y + 2y2 = 35 Solving -19y + 2y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + -19y + 2y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -19y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -9.5y + y2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -9.5y + 17.5 + y2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -9.5y + y2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -9.5y + y2 = 0 + 17.5 -9.5y + y2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -9.5y + y2 = 17.5 The y term is -9.5y. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5y + 22.5625 + y2 = 17.5 + 22.5625 Reorder the terms: 22.5625 + -9.5y + y2 = 17.5 + 22.5625 Combine like terms: 17.5 + 22.5625 = 40.0625 22.5625 + -9.5y + y2 = 40.0625 Factor a perfect square on the left side: (y + -4.75)(y + -4.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (y + -4.75) equal to 6.329494451 and -6.329494451.Subproblem 1
y + -4.75 = 6.329494451 Simplifying y + -4.75 = 6.329494451 Reorder the terms: -4.75 + y = 6.329494451 Solving -4.75 + y = 6.329494451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = 6.329494451 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = 6.329494451 + 4.75 y = 6.329494451 + 4.75 Combine like terms: 6.329494451 + 4.75 = 11.079494451 y = 11.079494451 Simplifying y = 11.079494451Subproblem 2
y + -4.75 = -6.329494451 Simplifying y + -4.75 = -6.329494451 Reorder the terms: -4.75 + y = -6.329494451 Solving -4.75 + y = -6.329494451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = -6.329494451 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = -6.329494451 + 4.75 y = -6.329494451 + 4.75 Combine like terms: -6.329494451 + 4.75 = -1.579494451 y = -1.579494451 Simplifying y = -1.579494451Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.079494451, -1.579494451}
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