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Simplifying 2y2 + -8y = 7 Reorder the terms: -8y + 2y2 = 7 Solving -8y + 2y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + -8y + 2y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -4y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -4y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -4y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -4y + y2 = 0 + 3.5 -4y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -4y + y2 = 3.5 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 = 3.5 + 4 Reorder the terms: 4 + -4y + y2 = 3.5 + 4 Combine like terms: 3.5 + 4 = 7.5 4 + -4y + y2 = 7.5 Factor a perfect square on the left side: (y + -2)(y + -2) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (y + -2) equal to 2.738612788 and -2.738612788.Subproblem 1
y + -2 = 2.738612788 Simplifying y + -2 = 2.738612788 Reorder the terms: -2 + y = 2.738612788 Solving -2 + y = 2.738612788 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 = 2.738612788 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.738612788 + 2 y = 2.738612788 + 2 Combine like terms: 2.738612788 + 2 = 4.738612788 y = 4.738612788 Simplifying y = 4.738612788Subproblem 2
y + -2 = -2.738612788 Simplifying y + -2 = -2.738612788 Reorder the terms: -2 + y = -2.738612788 Solving -2 + y = -2.738612788 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 = -2.738612788 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.738612788 + 2 y = -2.738612788 + 2 Combine like terms: -2.738612788 + 2 = -0.738612788 y = -0.738612788 Simplifying y = -0.738612788Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.738612788, -0.738612788}
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