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Simplifying -1Y2 + 12Y + 14 = 0 Reorder the terms: 14 + 12Y + -1Y2 = 0 Solving 14 + 12Y + -1Y2 = 0 Solving for variable 'Y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -12Y + Y2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -12Y + 14 + Y2 = 0 + 14 Reorder the terms: -14 + 14 + -12Y + Y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -12Y + Y2 = 0 + 14 -12Y + Y2 = 0 + 14 Combine like terms: 0 + 14 = 14 -12Y + Y2 = 14 The Y term is -12Y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12Y + 36 + Y2 = 14 + 36 Reorder the terms: 36 + -12Y + Y2 = 14 + 36 Combine like terms: 14 + 36 = 50 36 + -12Y + Y2 = 50 Factor a perfect square on the left side: (Y + -6)(Y + -6) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (Y + -6) equal to 7.071067812 and -7.071067812.Subproblem 1
Y + -6 = 7.071067812 Simplifying Y + -6 = 7.071067812 Reorder the terms: -6 + Y = 7.071067812 Solving -6 + Y = 7.071067812 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + Y = 7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + Y = 7.071067812 + 6 Y = 7.071067812 + 6 Combine like terms: 7.071067812 + 6 = 13.071067812 Y = 13.071067812 Simplifying Y = 13.071067812Subproblem 2
Y + -6 = -7.071067812 Simplifying Y + -6 = -7.071067812 Reorder the terms: -6 + Y = -7.071067812 Solving -6 + Y = -7.071067812 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + Y = -7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + Y = -7.071067812 + 6 Y = -7.071067812 + 6 Combine like terms: -7.071067812 + 6 = -1.071067812 Y = -1.071067812 Simplifying Y = -1.071067812Solution
The solution to the problem is based on the solutions from the subproblems. Y = {13.071067812, -1.071067812}
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