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Simplifying 12y + -1y2 = 30 Solving 12y + -1y2 = 30 Solving for variable 'y'. Reorder the terms: -30 + 12y + -1y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -12y + y2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12y + -30 + y2 = 0 + -30 Reorder the terms: 30 + -30 + -12y + y2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12y + y2 = 0 + -30 -12y + y2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12y + y2 = -30 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 = -30 + 36 Reorder the terms: 36 + -12y + y2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12y + y2 = 6 Factor a perfect square on the left side: (y + -6)(y + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
y + -6 = 2.449489743 Simplifying y + -6 = 2.449489743 Reorder the terms: -6 + y = 2.449489743 Solving -6 + y = 2.449489743 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 = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + y = 2.449489743 + 6 y = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 y = 8.449489743 Simplifying y = 8.449489743Subproblem 2
y + -6 = -2.449489743 Simplifying y + -6 = -2.449489743 Reorder the terms: -6 + y = -2.449489743 Solving -6 + y = -2.449489743 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 = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + y = -2.449489743 + 6 y = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 y = 3.550510257 Simplifying y = 3.550510257Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.449489743, 3.550510257}
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