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Simplifying y = -16y2 + 2704 Reorder the terms: y = 2704 + -16y2 Solving y = 2704 + -16y2 Solving for variable 'y'. Reorder the terms: -2704 + y + 16y2 = 2704 + -16y2 + -2704 + 16y2 Reorder the terms: -2704 + y + 16y2 = 2704 + -2704 + -16y2 + 16y2 Combine like terms: 2704 + -2704 = 0 -2704 + y + 16y2 = 0 + -16y2 + 16y2 -2704 + y + 16y2 = -16y2 + 16y2 Combine like terms: -16y2 + 16y2 = 0 -2704 + y + 16y2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -169 + 0.0625y + y2 = 0 Move the constant term to the right: Add '169' to each side of the equation. -169 + 0.0625y + 169 + y2 = 0 + 169 Reorder the terms: -169 + 169 + 0.0625y + y2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 0.0625y + y2 = 0 + 169 0.0625y + y2 = 0 + 169 Combine like terms: 0 + 169 = 169 0.0625y + y2 = 169 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625y + 0.25 + y2 = 169 + 0.25 Reorder the terms: 0.25 + 0.0625y + y2 = 169 + 0.25 Combine like terms: 169 + 0.25 = 169.25 0.25 + 0.0625y + y2 = 169.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 169.25 Calculate the square root of the right side: 13.009611831 Break this problem into two subproblems by setting (y + 0.5) equal to 13.009611831 and -13.009611831.Subproblem 1
y + 0.5 = 13.009611831 Simplifying y + 0.5 = 13.009611831 Reorder the terms: 0.5 + y = 13.009611831 Solving 0.5 + y = 13.009611831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 13.009611831 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 13.009611831 + -0.5 y = 13.009611831 + -0.5 Combine like terms: 13.009611831 + -0.5 = 12.509611831 y = 12.509611831 Simplifying y = 12.509611831Subproblem 2
y + 0.5 = -13.009611831 Simplifying y + 0.5 = -13.009611831 Reorder the terms: 0.5 + y = -13.009611831 Solving 0.5 + y = -13.009611831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -13.009611831 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -13.009611831 + -0.5 y = -13.009611831 + -0.5 Combine like terms: -13.009611831 + -0.5 = -13.509611831 y = -13.509611831 Simplifying y = -13.509611831Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.509611831, -13.509611831}
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