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Simplifying 6y(y + 6) = 90 Reorder the terms: 6y(6 + y) = 90 (6 * 6y + y * 6y) = 90 (36y + 6y2) = 90 Solving 36y + 6y2 = 90 Solving for variable 'y'. Reorder the terms: -90 + 36y + 6y2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 36y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 6y + y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-15 + 6y + y2)' equal to zero and attempt to solve: Simplifying -15 + 6y + y2 = 0 Solving -15 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 6y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6y + y2 = 0 + 15 6y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 6y + y2 = 15 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 15 + 9 Reorder the terms: 9 + 6y + y2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6y + y2 = 24 Factor a perfect square on the left side: (y + 3)(y + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
y + 3 = 4.898979486 Simplifying y + 3 = 4.898979486 Reorder the terms: 3 + y = 4.898979486 Solving 3 + y = 4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.898979486 + -3 y = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 y = 1.898979486 Simplifying y = 1.898979486Subproblem 2
y + 3 = -4.898979486 Simplifying y + 3 = -4.898979486 Reorder the terms: 3 + y = -4.898979486 Solving 3 + y = -4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.898979486 + -3 y = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 y = -7.898979486 Simplifying y = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.898979486, -7.898979486}Solution
y = {1.898979486, -7.898979486}
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