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Simplifying -8y(y + 4) = 10y + 4 Reorder the terms: -8y(4 + y) = 10y + 4 (4 * -8y + y * -8y) = 10y + 4 (-32y + -8y2) = 10y + 4 Reorder the terms: -32y + -8y2 = 4 + 10y Solving -32y + -8y2 = 4 + 10y Solving for variable 'y'. Reorder the terms: -4 + -32y + -10y + -8y2 = 4 + 10y + -4 + -10y Combine like terms: -32y + -10y = -42y -4 + -42y + -8y2 = 4 + 10y + -4 + -10y Reorder the terms: -4 + -42y + -8y2 = 4 + -4 + 10y + -10y Combine like terms: 4 + -4 = 0 -4 + -42y + -8y2 = 0 + 10y + -10y -4 + -42y + -8y2 = 10y + -10y Combine like terms: 10y + -10y = 0 -4 + -42y + -8y2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 21y + 4y2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 21y + 4y2)' equal to zero and attempt to solve: Simplifying 2 + 21y + 4y2 = 0 Solving 2 + 21y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 5.25y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 5.25y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 5.25y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 5.25y + y2 = 0 + -0.5 5.25y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 5.25y + y2 = -0.5 The y term is 5.25y. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25y + 6.890625 + y2 = -0.5 + 6.890625 Reorder the terms: 6.890625 + 5.25y + y2 = -0.5 + 6.890625 Combine like terms: -0.5 + 6.890625 = 6.390625 6.890625 + 5.25y + y2 = 6.390625 Factor a perfect square on the left side: (y + 2.625)(y + 2.625) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (y + 2.625) equal to 2.527968552 and -2.527968552.Subproblem 1
y + 2.625 = 2.527968552 Simplifying y + 2.625 = 2.527968552 Reorder the terms: 2.625 + y = 2.527968552 Solving 2.625 + y = 2.527968552 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + y = 2.527968552 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + y = 2.527968552 + -2.625 y = 2.527968552 + -2.625 Combine like terms: 2.527968552 + -2.625 = -0.097031448 y = -0.097031448 Simplifying y = -0.097031448Subproblem 2
y + 2.625 = -2.527968552 Simplifying y + 2.625 = -2.527968552 Reorder the terms: 2.625 + y = -2.527968552 Solving 2.625 + y = -2.527968552 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + y = -2.527968552 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + y = -2.527968552 + -2.625 y = -2.527968552 + -2.625 Combine like terms: -2.527968552 + -2.625 = -5.152968552 y = -5.152968552 Simplifying y = -5.152968552Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.097031448, -5.152968552}Solution
y = {-0.097031448, -5.152968552}
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