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Simplifying 9y2 + -216y + 700 = 0 Reorder the terms: 700 + -216y + 9y2 = 0 Solving 700 + -216y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 77.77777778 + -24y + y2 = 0 Move the constant term to the right: Add '-77.77777778' to each side of the equation. 77.77777778 + -24y + -77.77777778 + y2 = 0 + -77.77777778 Reorder the terms: 77.77777778 + -77.77777778 + -24y + y2 = 0 + -77.77777778 Combine like terms: 77.77777778 + -77.77777778 = 0.00000000 0.00000000 + -24y + y2 = 0 + -77.77777778 -24y + y2 = 0 + -77.77777778 Combine like terms: 0 + -77.77777778 = -77.77777778 -24y + y2 = -77.77777778 The y term is -24y. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24y + 144 + y2 = -77.77777778 + 144 Reorder the terms: 144 + -24y + y2 = -77.77777778 + 144 Combine like terms: -77.77777778 + 144 = 66.22222222 144 + -24y + y2 = 66.22222222 Factor a perfect square on the left side: (y + -12)(y + -12) = 66.22222222 Calculate the square root of the right side: 8.137703744 Break this problem into two subproblems by setting (y + -12) equal to 8.137703744 and -8.137703744.Subproblem 1
y + -12 = 8.137703744 Simplifying y + -12 = 8.137703744 Reorder the terms: -12 + y = 8.137703744 Solving -12 + y = 8.137703744 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 8.137703744 + 12 Combine like terms: -12 + 12 = 0 0 + y = 8.137703744 + 12 y = 8.137703744 + 12 Combine like terms: 8.137703744 + 12 = 20.137703744 y = 20.137703744 Simplifying y = 20.137703744Subproblem 2
y + -12 = -8.137703744 Simplifying y + -12 = -8.137703744 Reorder the terms: -12 + y = -8.137703744 Solving -12 + y = -8.137703744 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -8.137703744 + 12 Combine like terms: -12 + 12 = 0 0 + y = -8.137703744 + 12 y = -8.137703744 + 12 Combine like terms: -8.137703744 + 12 = 3.862296256 y = 3.862296256 Simplifying y = 3.862296256Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.137703744, 3.862296256}
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