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Simplifying 3y(y + 6) = 30 Reorder the terms: 3y(6 + y) = 30 (6 * 3y + y * 3y) = 30 (18y + 3y2) = 30 Solving 18y + 3y2 = 30 Solving for variable 'y'. Reorder the terms: -30 + 18y + 3y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 18y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 6y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 6y + y2)' equal to zero and attempt to solve: Simplifying -10 + 6y + y2 = 0 Solving -10 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 6y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + 6y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6y + y2 = 0 + 10 6y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 6y + y2 = 10 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 = 10 + 9 Reorder the terms: 9 + 6y + y2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + 6y + y2 = 19 Factor a perfect square on the left side: (y + 3)(y + 3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + 3) equal to 4.358898944 and -4.358898944.Subproblem 1
y + 3 = 4.358898944 Simplifying y + 3 = 4.358898944 Reorder the terms: 3 + y = 4.358898944 Solving 3 + y = 4.358898944 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 = 4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.358898944 + -3 y = 4.358898944 + -3 Combine like terms: 4.358898944 + -3 = 1.358898944 y = 1.358898944 Simplifying y = 1.358898944Subproblem 2
y + 3 = -4.358898944 Simplifying y + 3 = -4.358898944 Reorder the terms: 3 + y = -4.358898944 Solving 3 + y = -4.358898944 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 = -4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.358898944 + -3 y = -4.358898944 + -3 Combine like terms: -4.358898944 + -3 = -7.358898944 y = -7.358898944 Simplifying y = -7.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.358898944, -7.358898944}Solution
y = {1.358898944, -7.358898944}
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