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Simplifying 2y2 + -16y + -5 = 0 Reorder the terms: -5 + -16y + 2y2 = 0 Solving -5 + -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'. -2.5 + -8y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -8y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -8y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -8y + y2 = 0 + 2.5 -8y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -8y + y2 = 2.5 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 = 2.5 + 16 Reorder the terms: 16 + -8y + y2 = 2.5 + 16 Combine like terms: 2.5 + 16 = 18.5 16 + -8y + y2 = 18.5 Factor a perfect square on the left side: (y + -4)(y + -4) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (y + -4) equal to 4.301162634 and -4.301162634.Subproblem 1
y + -4 = 4.301162634 Simplifying y + -4 = 4.301162634 Reorder the terms: -4 + y = 4.301162634 Solving -4 + y = 4.301162634 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 = 4.301162634 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.301162634 + 4 y = 4.301162634 + 4 Combine like terms: 4.301162634 + 4 = 8.301162634 y = 8.301162634 Simplifying y = 8.301162634Subproblem 2
y + -4 = -4.301162634 Simplifying y + -4 = -4.301162634 Reorder the terms: -4 + y = -4.301162634 Solving -4 + y = -4.301162634 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 = -4.301162634 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.301162634 + 4 y = -4.301162634 + 4 Combine like terms: -4.301162634 + 4 = -0.301162634 y = -0.301162634 Simplifying y = -0.301162634Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.301162634, -0.301162634}
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