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Simplifying 3y(3y + 4) = 4(y + 2) Reorder the terms: 3y(4 + 3y) = 4(y + 2) (4 * 3y + 3y * 3y) = 4(y + 2) (12y + 9y2) = 4(y + 2) Reorder the terms: 12y + 9y2 = 4(2 + y) 12y + 9y2 = (2 * 4 + y * 4) 12y + 9y2 = (8 + 4y) Solving 12y + 9y2 = 8 + 4y Solving for variable 'y'. Reorder the terms: -8 + 12y + -4y + 9y2 = 8 + 4y + -8 + -4y Combine like terms: 12y + -4y = 8y -8 + 8y + 9y2 = 8 + 4y + -8 + -4y Reorder the terms: -8 + 8y + 9y2 = 8 + -8 + 4y + -4y Combine like terms: 8 + -8 = 0 -8 + 8y + 9y2 = 0 + 4y + -4y -8 + 8y + 9y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -8 + 8y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.8888888889y + y2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.8888888889y + 0.8888888889 + y2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.8888888889y + y2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.8888888889y + y2 = 0 + 0.8888888889 0.8888888889y + y2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.8888888889y + y2 = 0.8888888889 The y term is 0.8888888889y. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889y + 0.1975308642 + y2 = 0.8888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889y + y2 = 0.8888888889 + 0.1975308642 Combine like terms: 0.8888888889 + 0.1975308642 = 1.0864197531 0.1975308642 + 0.8888888889y + y2 = 1.0864197531 Factor a perfect square on the left side: (y + 0.4444444445)(y + 0.4444444445) = 1.0864197531 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (y + 0.4444444445) equal to 1.042314613 and -1.042314613.Subproblem 1
y + 0.4444444445 = 1.042314613 Simplifying y + 0.4444444445 = 1.042314613 Reorder the terms: 0.4444444445 + y = 1.042314613 Solving 0.4444444445 + y = 1.042314613 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + y = 1.042314613 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + y = 1.042314613 + -0.4444444445 y = 1.042314613 + -0.4444444445 Combine like terms: 1.042314613 + -0.4444444445 = 0.5978701685 y = 0.5978701685 Simplifying y = 0.5978701685Subproblem 2
y + 0.4444444445 = -1.042314613 Simplifying y + 0.4444444445 = -1.042314613 Reorder the terms: 0.4444444445 + y = -1.042314613 Solving 0.4444444445 + y = -1.042314613 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + y = -1.042314613 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + y = -1.042314613 + -0.4444444445 y = -1.042314613 + -0.4444444445 Combine like terms: -1.042314613 + -0.4444444445 = -1.4867590575 y = -1.4867590575 Simplifying y = -1.4867590575Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5978701685, -1.4867590575}
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