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Simplifying 8y(2y + -3) = 3(5y + -7) Reorder the terms: 8y(-3 + 2y) = 3(5y + -7) (-3 * 8y + 2y * 8y) = 3(5y + -7) (-24y + 16y2) = 3(5y + -7) Reorder the terms: -24y + 16y2 = 3(-7 + 5y) -24y + 16y2 = (-7 * 3 + 5y * 3) -24y + 16y2 = (-21 + 15y) Solving -24y + 16y2 = -21 + 15y Solving for variable 'y'. Reorder the terms: 21 + -24y + -15y + 16y2 = -21 + 15y + 21 + -15y Combine like terms: -24y + -15y = -39y 21 + -39y + 16y2 = -21 + 15y + 21 + -15y Reorder the terms: 21 + -39y + 16y2 = -21 + 21 + 15y + -15y Combine like terms: -21 + 21 = 0 21 + -39y + 16y2 = 0 + 15y + -15y 21 + -39y + 16y2 = 15y + -15y Combine like terms: 15y + -15y = 0 21 + -39y + 16y2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.3125 + -2.4375y + y2 = 0 Move the constant term to the right: Add '-1.3125' to each side of the equation. 1.3125 + -2.4375y + -1.3125 + y2 = 0 + -1.3125 Reorder the terms: 1.3125 + -1.3125 + -2.4375y + y2 = 0 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + -2.4375y + y2 = 0 + -1.3125 -2.4375y + y2 = 0 + -1.3125 Combine like terms: 0 + -1.3125 = -1.3125 -2.4375y + y2 = -1.3125 The y term is -2.4375y. Take half its coefficient (-1.21875). Square it (1.485351563) and add it to both sides. Add '1.485351563' to each side of the equation. -2.4375y + 1.485351563 + y2 = -1.3125 + 1.485351563 Reorder the terms: 1.485351563 + -2.4375y + y2 = -1.3125 + 1.485351563 Combine like terms: -1.3125 + 1.485351563 = 0.172851563 1.485351563 + -2.4375y + y2 = 0.172851563 Factor a perfect square on the left side: (y + -1.21875)(y + -1.21875) = 0.172851563 Calculate the square root of the right side: 0.41575421 Break this problem into two subproblems by setting (y + -1.21875) equal to 0.41575421 and -0.41575421.Subproblem 1
y + -1.21875 = 0.41575421 Simplifying y + -1.21875 = 0.41575421 Reorder the terms: -1.21875 + y = 0.41575421 Solving -1.21875 + y = 0.41575421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + y = 0.41575421 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + y = 0.41575421 + 1.21875 y = 0.41575421 + 1.21875 Combine like terms: 0.41575421 + 1.21875 = 1.63450421 y = 1.63450421 Simplifying y = 1.63450421Subproblem 2
y + -1.21875 = -0.41575421 Simplifying y + -1.21875 = -0.41575421 Reorder the terms: -1.21875 + y = -0.41575421 Solving -1.21875 + y = -0.41575421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + y = -0.41575421 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + y = -0.41575421 + 1.21875 y = -0.41575421 + 1.21875 Combine like terms: -0.41575421 + 1.21875 = 0.80299579 y = 0.80299579 Simplifying y = 0.80299579Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.63450421, 0.80299579}
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