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Simplifying -5y + -2y(y + 4) = 6y + -9 Reorder the terms: -5y + -2y(4 + y) = 6y + -9 -5y + (4 * -2y + y * -2y) = 6y + -9 -5y + (-8y + -2y2) = 6y + -9 Combine like terms: -5y + -8y = -13y -13y + -2y2 = 6y + -9 Reorder the terms: -13y + -2y2 = -9 + 6y Solving -13y + -2y2 = -9 + 6y Solving for variable 'y'. Reorder the terms: 9 + -13y + -6y + -2y2 = -9 + 6y + 9 + -6y Combine like terms: -13y + -6y = -19y 9 + -19y + -2y2 = -9 + 6y + 9 + -6y Reorder the terms: 9 + -19y + -2y2 = -9 + 9 + 6y + -6y Combine like terms: -9 + 9 = 0 9 + -19y + -2y2 = 0 + 6y + -6y 9 + -19y + -2y2 = 6y + -6y Combine like terms: 6y + -6y = 0 9 + -19y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 9.5y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 9.5y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 9.5y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 9.5y + y2 = 0 + 4.5 9.5y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 9.5y + y2 = 4.5 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 = 4.5 + 22.5625 Reorder the terms: 22.5625 + 9.5y + y2 = 4.5 + 22.5625 Combine like terms: 4.5 + 22.5625 = 27.0625 22.5625 + 9.5y + y2 = 27.0625 Factor a perfect square on the left side: (y + 4.75)(y + 4.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (y + 4.75) equal to 5.202163012 and -5.202163012.Subproblem 1
y + 4.75 = 5.202163012 Simplifying y + 4.75 = 5.202163012 Reorder the terms: 4.75 + y = 5.202163012 Solving 4.75 + y = 5.202163012 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 = 5.202163012 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + y = 5.202163012 + -4.75 y = 5.202163012 + -4.75 Combine like terms: 5.202163012 + -4.75 = 0.452163012 y = 0.452163012 Simplifying y = 0.452163012Subproblem 2
y + 4.75 = -5.202163012 Simplifying y + 4.75 = -5.202163012 Reorder the terms: 4.75 + y = -5.202163012 Solving 4.75 + y = -5.202163012 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 = -5.202163012 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + y = -5.202163012 + -4.75 y = -5.202163012 + -4.75 Combine like terms: -5.202163012 + -4.75 = -9.952163012 y = -9.952163012 Simplifying y = -9.952163012Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.452163012, -9.952163012}
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