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Simplifying 0.36y2 + 5.04y + -27.36 = 0 Reorder the terms: -27.36 + 5.04y + 0.36y2 = 0 Solving -27.36 + 5.04y + 0.36y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. -76 + 14y + y2 = 0 Move the constant term to the right: Add '76' to each side of the equation. -76 + 14y + 76 + y2 = 0 + 76 Reorder the terms: -76 + 76 + 14y + y2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 14y + y2 = 0 + 76 14y + y2 = 0 + 76 Combine like terms: 0 + 76 = 76 14y + y2 = 76 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = 76 + 49 Reorder the terms: 49 + 14y + y2 = 76 + 49 Combine like terms: 76 + 49 = 125 49 + 14y + y2 = 125 Factor a perfect square on the left side: (y + 7)(y + 7) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (y + 7) equal to 11.180339887 and -11.180339887.Subproblem 1
y + 7 = 11.180339887 Simplifying y + 7 = 11.180339887 Reorder the terms: 7 + y = 11.180339887 Solving 7 + y = 11.180339887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + y = 11.180339887 + -7 y = 11.180339887 + -7 Combine like terms: 11.180339887 + -7 = 4.180339887 y = 4.180339887 Simplifying y = 4.180339887Subproblem 2
y + 7 = -11.180339887 Simplifying y + 7 = -11.180339887 Reorder the terms: 7 + y = -11.180339887 Solving 7 + y = -11.180339887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = -11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + y = -11.180339887 + -7 y = -11.180339887 + -7 Combine like terms: -11.180339887 + -7 = -18.180339887 y = -18.180339887 Simplifying y = -18.180339887Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.180339887, -18.180339887}
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