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Simplifying 5y2 + -6y = 36 Reorder the terms: -6y + 5y2 = 36 Solving -6y + 5y2 = 36 Solving for variable 'y'. Reorder the terms: -36 + -6y + 5y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -6y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -1.2y + y2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -1.2y + 7.2 + y2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -1.2y + y2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -1.2y + y2 = 0 + 7.2 -1.2y + y2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -1.2y + y2 = 7.2 The y term is -1.2y. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2y + 0.36 + y2 = 7.2 + 0.36 Reorder the terms: 0.36 + -1.2y + y2 = 7.2 + 0.36 Combine like terms: 7.2 + 0.36 = 7.56 0.36 + -1.2y + y2 = 7.56 Factor a perfect square on the left side: (y + -0.6)(y + -0.6) = 7.56 Calculate the square root of the right side: 2.749545417 Break this problem into two subproblems by setting (y + -0.6) equal to 2.749545417 and -2.749545417.Subproblem 1
y + -0.6 = 2.749545417 Simplifying y + -0.6 = 2.749545417 Reorder the terms: -0.6 + y = 2.749545417 Solving -0.6 + y = 2.749545417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = 2.749545417 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = 2.749545417 + 0.6 y = 2.749545417 + 0.6 Combine like terms: 2.749545417 + 0.6 = 3.349545417 y = 3.349545417 Simplifying y = 3.349545417Subproblem 2
y + -0.6 = -2.749545417 Simplifying y + -0.6 = -2.749545417 Reorder the terms: -0.6 + y = -2.749545417 Solving -0.6 + y = -2.749545417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = -2.749545417 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = -2.749545417 + 0.6 y = -2.749545417 + 0.6 Combine like terms: -2.749545417 + 0.6 = -2.149545417 y = -2.149545417 Simplifying y = -2.149545417Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.349545417, -2.149545417}
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