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Simplifying 4y2 + 37y + -15 = 0 Reorder the terms: -15 + 37y + 4y2 = 0 Solving -15 + 37y + 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'. -3.75 + 9.25y + y2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 9.25y + 3.75 + y2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 9.25y + y2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 9.25y + y2 = 0 + 3.75 9.25y + y2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 9.25y + y2 = 3.75 The y term is 9.25y. Take half its coefficient (4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. 9.25y + 21.390625 + y2 = 3.75 + 21.390625 Reorder the terms: 21.390625 + 9.25y + y2 = 3.75 + 21.390625 Combine like terms: 3.75 + 21.390625 = 25.140625 21.390625 + 9.25y + y2 = 25.140625 Factor a perfect square on the left side: (y + 4.625)(y + 4.625) = 25.140625 Calculate the square root of the right side: 5.01404278 Break this problem into two subproblems by setting (y + 4.625) equal to 5.01404278 and -5.01404278.Subproblem 1
y + 4.625 = 5.01404278 Simplifying y + 4.625 = 5.01404278 Reorder the terms: 4.625 + y = 5.01404278 Solving 4.625 + y = 5.01404278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + y = 5.01404278 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + y = 5.01404278 + -4.625 y = 5.01404278 + -4.625 Combine like terms: 5.01404278 + -4.625 = 0.38904278 y = 0.38904278 Simplifying y = 0.38904278Subproblem 2
y + 4.625 = -5.01404278 Simplifying y + 4.625 = -5.01404278 Reorder the terms: 4.625 + y = -5.01404278 Solving 4.625 + y = -5.01404278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + y = -5.01404278 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + y = -5.01404278 + -4.625 y = -5.01404278 + -4.625 Combine like terms: -5.01404278 + -4.625 = -9.63904278 y = -9.63904278 Simplifying y = -9.63904278Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.38904278, -9.63904278}
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