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Simplifying -1y2 + 8y = 3 Reorder the terms: 8y + -1y2 = 3 Solving 8y + -1y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + 8y + -1y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -8y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -8y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8y + y2 = 0 + -3 -8y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8y + y2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8y + y2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8y + y2 = 13 Factor a perfect square on the left side: (y + -4)(y + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
y + -4 = 3.605551275 Simplifying y + -4 = 3.605551275 Reorder the terms: -4 + y = 3.605551275 Solving -4 + y = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + y = 3.605551275 + 4 y = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 y = 7.605551275 Simplifying y = 7.605551275Subproblem 2
y + -4 = -3.605551275 Simplifying y + -4 = -3.605551275 Reorder the terms: -4 + y = -3.605551275 Solving -4 + y = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + y = -3.605551275 + 4 y = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 y = 0.394448725 Simplifying y = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.605551275, 0.394448725}
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