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Simplifying 8y2 + -8y + -36 = 0 Reorder the terms: -36 + -8y + 8y2 = 0 Solving -36 + -8y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -2y + 2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -2y + 2y2)' equal to zero and attempt to solve: Simplifying -9 + -2y + 2y2 = 0 Solving -9 + -2y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -1y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1y + y2 = 0 + 4.5 -1y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1y + y2 = 4.5 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 4.5 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -1y + y2 = 4.75 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (y + -0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
y + -0.5 = 2.179449472 Simplifying y + -0.5 = 2.179449472 Reorder the terms: -0.5 + y = 2.179449472 Solving -0.5 + y = 2.179449472 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 2.179449472 + 0.5 y = 2.179449472 + 0.5 Combine like terms: 2.179449472 + 0.5 = 2.679449472 y = 2.679449472 Simplifying y = 2.679449472Subproblem 2
y + -0.5 = -2.179449472 Simplifying y + -0.5 = -2.179449472 Reorder the terms: -0.5 + y = -2.179449472 Solving -0.5 + y = -2.179449472 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -2.179449472 + 0.5 y = -2.179449472 + 0.5 Combine like terms: -2.179449472 + 0.5 = -1.679449472 y = -1.679449472 Simplifying y = -1.679449472Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.679449472, -1.679449472}Solution
y = {2.679449472, -1.679449472}
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