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Simplifying (5y + 6)(5y + 6) = 24 Reorder the terms: (6 + 5y)(5y + 6) = 24 Reorder the terms: (6 + 5y)(6 + 5y) = 24 Multiply (6 + 5y) * (6 + 5y) (6(6 + 5y) + 5y * (6 + 5y)) = 24 ((6 * 6 + 5y * 6) + 5y * (6 + 5y)) = 24 ((36 + 30y) + 5y * (6 + 5y)) = 24 (36 + 30y + (6 * 5y + 5y * 5y)) = 24 (36 + 30y + (30y + 25y2)) = 24 Combine like terms: 30y + 30y = 60y (36 + 60y + 25y2) = 24 Solving 36 + 60y + 25y2 = 24 Solving for variable 'y'. Reorder the terms: 36 + -24 + 60y + 25y2 = 24 + -24 Combine like terms: 36 + -24 = 12 12 + 60y + 25y2 = 24 + -24 Combine like terms: 24 + -24 = 0 12 + 60y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.48 + 2.4y + y2 = 0 Move the constant term to the right: Add '-0.48' to each side of the equation. 0.48 + 2.4y + -0.48 + y2 = 0 + -0.48 Reorder the terms: 0.48 + -0.48 + 2.4y + y2 = 0 + -0.48 Combine like terms: 0.48 + -0.48 = 0.00 0.00 + 2.4y + y2 = 0 + -0.48 2.4y + y2 = 0 + -0.48 Combine like terms: 0 + -0.48 = -0.48 2.4y + y2 = -0.48 The y term is 2.4y. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4y + 1.44 + y2 = -0.48 + 1.44 Reorder the terms: 1.44 + 2.4y + y2 = -0.48 + 1.44 Combine like terms: -0.48 + 1.44 = 0.96 1.44 + 2.4y + y2 = 0.96 Factor a perfect square on the left side: (y + 1.2)(y + 1.2) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (y + 1.2) equal to 0.979795897 and -0.979795897.Subproblem 1
y + 1.2 = 0.979795897 Simplifying y + 1.2 = 0.979795897 Reorder the terms: 1.2 + y = 0.979795897 Solving 1.2 + y = 0.979795897 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = 0.979795897 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = 0.979795897 + -1.2 y = 0.979795897 + -1.2 Combine like terms: 0.979795897 + -1.2 = -0.220204103 y = -0.220204103 Simplifying y = -0.220204103Subproblem 2
y + 1.2 = -0.979795897 Simplifying y + 1.2 = -0.979795897 Reorder the terms: 1.2 + y = -0.979795897 Solving 1.2 + y = -0.979795897 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = -0.979795897 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = -0.979795897 + -1.2 y = -0.979795897 + -1.2 Combine like terms: -0.979795897 + -1.2 = -2.179795897 y = -2.179795897 Simplifying y = -2.179795897Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.220204103, -2.179795897}
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