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Simplifying 2y2 + -1y = 4 Reorder the terms: -1y + 2y2 = 4 Solving -1y + 2y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -1y + 2y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -1y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -0.5y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.5y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -0.5y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.5y + y2 = 0 + 2 -0.5y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.5y + y2 = 2 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = 2 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + -0.5y + y2 = 2.0625 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (y + -0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
y + -0.25 = 1.436140662 Simplifying y + -0.25 = 1.436140662 Reorder the terms: -0.25 + y = 1.436140662 Solving -0.25 + y = 1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 1.436140662 + 0.25 y = 1.436140662 + 0.25 Combine like terms: 1.436140662 + 0.25 = 1.686140662 y = 1.686140662 Simplifying y = 1.686140662Subproblem 2
y + -0.25 = -1.436140662 Simplifying y + -0.25 = -1.436140662 Reorder the terms: -0.25 + y = -1.436140662 Solving -0.25 + y = -1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -1.436140662 + 0.25 y = -1.436140662 + 0.25 Combine like terms: -1.436140662 + 0.25 = -1.186140662 y = -1.186140662 Simplifying y = -1.186140662Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.686140662, -1.186140662}
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