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Simplifying 5y + -4y(y + -6) + 3 = 9 Reorder the terms: 5y + -4y(-6 + y) + 3 = 9 5y + (-6 * -4y + y * -4y) + 3 = 9 5y + (24y + -4y2) + 3 = 9 Reorder the terms: 3 + 5y + 24y + -4y2 = 9 Combine like terms: 5y + 24y = 29y 3 + 29y + -4y2 = 9 Solving 3 + 29y + -4y2 = 9 Solving for variable 'y'. Reorder the terms: 3 + -9 + 29y + -4y2 = 9 + -9 Combine like terms: 3 + -9 = -6 -6 + 29y + -4y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -6 + 29y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.5 + -7.25y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -7.25y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -7.25y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -7.25y + y2 = 0 + -1.5 -7.25y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -7.25y + y2 = -1.5 The y term is -7.25y. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25y + 13.140625 + y2 = -1.5 + 13.140625 Reorder the terms: 13.140625 + -7.25y + y2 = -1.5 + 13.140625 Combine like terms: -1.5 + 13.140625 = 11.640625 13.140625 + -7.25y + y2 = 11.640625 Factor a perfect square on the left side: (y + -3.625)(y + -3.625) = 11.640625 Calculate the square root of the right side: 3.411836016 Break this problem into two subproblems by setting (y + -3.625) equal to 3.411836016 and -3.411836016.Subproblem 1
y + -3.625 = 3.411836016 Simplifying y + -3.625 = 3.411836016 Reorder the terms: -3.625 + y = 3.411836016 Solving -3.625 + y = 3.411836016 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + y = 3.411836016 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + y = 3.411836016 + 3.625 y = 3.411836016 + 3.625 Combine like terms: 3.411836016 + 3.625 = 7.036836016 y = 7.036836016 Simplifying y = 7.036836016Subproblem 2
y + -3.625 = -3.411836016 Simplifying y + -3.625 = -3.411836016 Reorder the terms: -3.625 + y = -3.411836016 Solving -3.625 + y = -3.411836016 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + y = -3.411836016 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + y = -3.411836016 + 3.625 y = -3.411836016 + 3.625 Combine like terms: -3.411836016 + 3.625 = 0.213163984 y = 0.213163984 Simplifying y = 0.213163984Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.036836016, 0.213163984}
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