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Simplifying y(4y + -3) = 4(2y + 6) Reorder the terms: y(-3 + 4y) = 4(2y + 6) (-3 * y + 4y * y) = 4(2y + 6) (-3y + 4y2) = 4(2y + 6) Reorder the terms: -3y + 4y2 = 4(6 + 2y) -3y + 4y2 = (6 * 4 + 2y * 4) -3y + 4y2 = (24 + 8y) Solving -3y + 4y2 = 24 + 8y Solving for variable 'y'. Reorder the terms: -24 + -3y + -8y + 4y2 = 24 + 8y + -24 + -8y Combine like terms: -3y + -8y = -11y -24 + -11y + 4y2 = 24 + 8y + -24 + -8y Reorder the terms: -24 + -11y + 4y2 = 24 + -24 + 8y + -8y Combine like terms: 24 + -24 = 0 -24 + -11y + 4y2 = 0 + 8y + -8y -24 + -11y + 4y2 = 8y + -8y Combine like terms: 8y + -8y = 0 -24 + -11y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + -2.75y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.75y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -2.75y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.75y + y2 = 0 + 6 -2.75y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.75y + y2 = 6 The y term is -2.75y. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75y + 1.890625 + y2 = 6 + 1.890625 Reorder the terms: 1.890625 + -2.75y + y2 = 6 + 1.890625 Combine like terms: 6 + 1.890625 = 7.890625 1.890625 + -2.75y + y2 = 7.890625 Factor a perfect square on the left side: (y + -1.375)(y + -1.375) = 7.890625 Calculate the square root of the right side: 2.809025632 Break this problem into two subproblems by setting (y + -1.375) equal to 2.809025632 and -2.809025632.Subproblem 1
y + -1.375 = 2.809025632 Simplifying y + -1.375 = 2.809025632 Reorder the terms: -1.375 + y = 2.809025632 Solving -1.375 + y = 2.809025632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = 2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = 2.809025632 + 1.375 y = 2.809025632 + 1.375 Combine like terms: 2.809025632 + 1.375 = 4.184025632 y = 4.184025632 Simplifying y = 4.184025632Subproblem 2
y + -1.375 = -2.809025632 Simplifying y + -1.375 = -2.809025632 Reorder the terms: -1.375 + y = -2.809025632 Solving -1.375 + y = -2.809025632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = -2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = -2.809025632 + 1.375 y = -2.809025632 + 1.375 Combine like terms: -2.809025632 + 1.375 = -1.434025632 y = -1.434025632 Simplifying y = -1.434025632Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.184025632, -1.434025632}
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