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Simplifying -2y2 + 8y + 86 = 0 Reorder the terms: 86 + 8y + -2y2 = 0 Solving 86 + 8y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(43 + 4y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + 4y + -1y2)' equal to zero and attempt to solve: Simplifying 43 + 4y + -1y2 = 0 Solving 43 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + -4y + y2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + -4y + 43 + y2 = 0 + 43 Reorder the terms: -43 + 43 + -4y + y2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -4y + y2 = 0 + 43 -4y + y2 = 0 + 43 Combine like terms: 0 + 43 = 43 -4y + y2 = 43 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 43 + 4 Reorder the terms: 4 + -4y + y2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + -4y + y2 = 47 Factor a perfect square on the left side: (y + -2)(y + -2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (y + -2) equal to 6.8556546 and -6.8556546.Subproblem 1
y + -2 = 6.8556546 Simplifying y + -2 = 6.8556546 Reorder the terms: -2 + y = 6.8556546 Solving -2 + y = 6.8556546 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + y = 6.8556546 + 2 y = 6.8556546 + 2 Combine like terms: 6.8556546 + 2 = 8.8556546 y = 8.8556546 Simplifying y = 8.8556546Subproblem 2
y + -2 = -6.8556546 Simplifying y + -2 = -6.8556546 Reorder the terms: -2 + y = -6.8556546 Solving -2 + y = -6.8556546 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + y = -6.8556546 + 2 y = -6.8556546 + 2 Combine like terms: -6.8556546 + 2 = -4.8556546 y = -4.8556546 Simplifying y = -4.8556546Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.8556546, -4.8556546}Solution
y = {8.8556546, -4.8556546}
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