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Simplifying 8y2 + 18y = 36 Reorder the terms: 18y + 8y2 = 36 Solving 18y + 8y2 = 36 Solving for variable 'y'. Reorder the terms: -36 + 18y + 8y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 18y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 9y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 9y + 4y2)' equal to zero and attempt to solve: Simplifying -18 + 9y + 4y2 = 0 Solving -18 + 9y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 2.25y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2.25y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2.25y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2.25y + y2 = 0 + 4.5 2.25y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2.25y + y2 = 4.5 The y term is 2.25y. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25y + 1.265625 + y2 = 4.5 + 1.265625 Reorder the terms: 1.265625 + 2.25y + y2 = 4.5 + 1.265625 Combine like terms: 4.5 + 1.265625 = 5.765625 1.265625 + 2.25y + y2 = 5.765625 Factor a perfect square on the left side: (y + 1.125)(y + 1.125) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (y + 1.125) equal to 2.401171589 and -2.401171589.Subproblem 1
y + 1.125 = 2.401171589 Simplifying y + 1.125 = 2.401171589 Reorder the terms: 1.125 + y = 2.401171589 Solving 1.125 + y = 2.401171589 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = 2.401171589 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = 2.401171589 + -1.125 y = 2.401171589 + -1.125 Combine like terms: 2.401171589 + -1.125 = 1.276171589 y = 1.276171589 Simplifying y = 1.276171589Subproblem 2
y + 1.125 = -2.401171589 Simplifying y + 1.125 = -2.401171589 Reorder the terms: 1.125 + y = -2.401171589 Solving 1.125 + y = -2.401171589 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = -2.401171589 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = -2.401171589 + -1.125 y = -2.401171589 + -1.125 Combine like terms: -2.401171589 + -1.125 = -3.526171589 y = -3.526171589 Simplifying y = -3.526171589Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.276171589, -3.526171589}Solution
y = {1.276171589, -3.526171589}
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