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Simplifying 2y2 + -16y + -39 = 0 Reorder the terms: -39 + -16y + 2y2 = 0 Solving -39 + -16y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -8y + y2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -8y + 19.5 + y2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -8y + y2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -8y + y2 = 0 + 19.5 -8y + y2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -8y + y2 = 19.5 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 19.5 + 16 Reorder the terms: 16 + -8y + y2 = 19.5 + 16 Combine like terms: 19.5 + 16 = 35.5 16 + -8y + y2 = 35.5 Factor a perfect square on the left side: (y + -4)(y + -4) = 35.5 Calculate the square root of the right side: 5.958187644 Break this problem into two subproblems by setting (y + -4) equal to 5.958187644 and -5.958187644.Subproblem 1
y + -4 = 5.958187644 Simplifying y + -4 = 5.958187644 Reorder the terms: -4 + y = 5.958187644 Solving -4 + y = 5.958187644 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 5.958187644 + 4 Combine like terms: -4 + 4 = 0 0 + y = 5.958187644 + 4 y = 5.958187644 + 4 Combine like terms: 5.958187644 + 4 = 9.958187644 y = 9.958187644 Simplifying y = 9.958187644Subproblem 2
y + -4 = -5.958187644 Simplifying y + -4 = -5.958187644 Reorder the terms: -4 + y = -5.958187644 Solving -4 + y = -5.958187644 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -5.958187644 + 4 Combine like terms: -4 + 4 = 0 0 + y = -5.958187644 + 4 y = -5.958187644 + 4 Combine like terms: -5.958187644 + 4 = -1.958187644 y = -1.958187644 Simplifying y = -1.958187644Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.958187644, -1.958187644}
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