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Simplifying -4y + 2y2 = 35 Solving -4y + 2y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + -4y + 2y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -2y + y2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -2y + 17.5 + y2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -2y + y2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -2y + y2 = 0 + 17.5 -2y + y2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -2y + y2 = 17.5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 17.5 + 1 Reorder the terms: 1 + -2y + y2 = 17.5 + 1 Combine like terms: 17.5 + 1 = 18.5 1 + -2y + y2 = 18.5 Factor a perfect square on the left side: (y + -1)(y + -1) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (y + -1) equal to 4.301162634 and -4.301162634.Subproblem 1
y + -1 = 4.301162634 Simplifying y + -1 = 4.301162634 Reorder the terms: -1 + y = 4.301162634 Solving -1 + y = 4.301162634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.301162634 + 1 y = 4.301162634 + 1 Combine like terms: 4.301162634 + 1 = 5.301162634 y = 5.301162634 Simplifying y = 5.301162634Subproblem 2
y + -1 = -4.301162634 Simplifying y + -1 = -4.301162634 Reorder the terms: -1 + y = -4.301162634 Solving -1 + y = -4.301162634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.301162634 + 1 y = -4.301162634 + 1 Combine like terms: -4.301162634 + 1 = -3.301162634 y = -3.301162634 Simplifying y = -3.301162634Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.301162634, -3.301162634}
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