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Simplifying 4 + -4y + -1y2 = 0 Solving 4 + -4y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 4y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 4y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4y + y2 = 0 + 4 4y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 4y + y2 = 4 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 = 4 + 4 Reorder the terms: 4 + 4y + y2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4y + y2 = 8 Factor a perfect square on the left side: (y + 2)(y + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
y + 2 = 2.828427125 Simplifying y + 2 = 2.828427125 Reorder the terms: 2 + y = 2.828427125 Solving 2 + y = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.828427125 + -2 y = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 y = 0.828427125 Simplifying y = 0.828427125Subproblem 2
y + 2 = -2.828427125 Simplifying y + 2 = -2.828427125 Reorder the terms: 2 + y = -2.828427125 Solving 2 + y = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.828427125 + -2 y = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 y = -4.828427125 Simplifying y = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.828427125, -4.828427125}
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