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Simplifying 0 = -5y2 + 24y + 48 Reorder the terms: 0 = 48 + 24y + -5y2 Solving 0 = 48 + 24y + -5y2 Solving for variable 'y'. Combine like terms: 0 + -48 = -48 -48 + -24y + 5y2 = 48 + 24y + -5y2 + -48 + -24y + 5y2 Reorder the terms: -48 + -24y + 5y2 = 48 + -48 + 24y + -24y + -5y2 + 5y2 Combine like terms: 48 + -48 = 0 -48 + -24y + 5y2 = 0 + 24y + -24y + -5y2 + 5y2 -48 + -24y + 5y2 = 24y + -24y + -5y2 + 5y2 Combine like terms: 24y + -24y = 0 -48 + -24y + 5y2 = 0 + -5y2 + 5y2 -48 + -24y + 5y2 = -5y2 + 5y2 Combine like terms: -5y2 + 5y2 = 0 -48 + -24y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + -4.8y + y2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -4.8y + 9.6 + y2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -4.8y + y2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -4.8y + y2 = 0 + 9.6 -4.8y + y2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -4.8y + y2 = 9.6 The y term is -4.8y. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8y + 5.76 + y2 = 9.6 + 5.76 Reorder the terms: 5.76 + -4.8y + y2 = 9.6 + 5.76 Combine like terms: 9.6 + 5.76 = 15.36 5.76 + -4.8y + y2 = 15.36 Factor a perfect square on the left side: (y + -2.4)(y + -2.4) = 15.36 Calculate the square root of the right side: 3.919183588 Break this problem into two subproblems by setting (y + -2.4) equal to 3.919183588 and -3.919183588.Subproblem 1
y + -2.4 = 3.919183588 Simplifying y + -2.4 = 3.919183588 Reorder the terms: -2.4 + y = 3.919183588 Solving -2.4 + y = 3.919183588 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = 3.919183588 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = 3.919183588 + 2.4 y = 3.919183588 + 2.4 Combine like terms: 3.919183588 + 2.4 = 6.319183588 y = 6.319183588 Simplifying y = 6.319183588Subproblem 2
y + -2.4 = -3.919183588 Simplifying y + -2.4 = -3.919183588 Reorder the terms: -2.4 + y = -3.919183588 Solving -2.4 + y = -3.919183588 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = -3.919183588 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = -3.919183588 + 2.4 y = -3.919183588 + 2.4 Combine like terms: -3.919183588 + 2.4 = -1.519183588 y = -1.519183588 Simplifying y = -1.519183588Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.319183588, -1.519183588}
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