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Simplifying 4y2 + -35y + 10 = 0 Reorder the terms: 10 + -35y + 4y2 = 0 Solving 10 + -35y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -8.75y + y2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -8.75y + -2.5 + y2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -8.75y + y2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -8.75y + y2 = 0 + -2.5 -8.75y + y2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -8.75y + y2 = -2.5 The y term is -8.75y. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75y + 19.140625 + y2 = -2.5 + 19.140625 Reorder the terms: 19.140625 + -8.75y + y2 = -2.5 + 19.140625 Combine like terms: -2.5 + 19.140625 = 16.640625 19.140625 + -8.75y + y2 = 16.640625 Factor a perfect square on the left side: (y + -4.375)(y + -4.375) = 16.640625 Calculate the square root of the right side: 4.079292218 Break this problem into two subproblems by setting (y + -4.375) equal to 4.079292218 and -4.079292218.Subproblem 1
y + -4.375 = 4.079292218 Simplifying y + -4.375 = 4.079292218 Reorder the terms: -4.375 + y = 4.079292218 Solving -4.375 + y = 4.079292218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + y = 4.079292218 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + y = 4.079292218 + 4.375 y = 4.079292218 + 4.375 Combine like terms: 4.079292218 + 4.375 = 8.454292218 y = 8.454292218 Simplifying y = 8.454292218Subproblem 2
y + -4.375 = -4.079292218 Simplifying y + -4.375 = -4.079292218 Reorder the terms: -4.375 + y = -4.079292218 Solving -4.375 + y = -4.079292218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + y = -4.079292218 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + y = -4.079292218 + 4.375 y = -4.079292218 + 4.375 Combine like terms: -4.079292218 + 4.375 = 0.295707782 y = 0.295707782 Simplifying y = 0.295707782Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.454292218, 0.295707782}
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