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Simplifying -2y + -3y2 + -7 + 4y2 = 0 Reorder the terms: -7 + -2y + -3y2 + 4y2 = 0 Combine like terms: -3y2 + 4y2 = 1y2 -7 + -2y + 1y2 = 0 Solving -7 + -2y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -2y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2y + y2 = 0 + 7 -2y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2y + y2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2y + y2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2y + y2 = 8 Factor a perfect square on the left side: (y + -1)(y + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
y + -1 = 2.828427125 Simplifying y + -1 = 2.828427125 Reorder the terms: -1 + y = 2.828427125 Solving -1 + y = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.828427125 + 1 y = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 y = 3.828427125 Simplifying y = 3.828427125Subproblem 2
y + -1 = -2.828427125 Simplifying y + -1 = -2.828427125 Reorder the terms: -1 + y = -2.828427125 Solving -1 + y = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.828427125 + 1 y = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 y = -1.828427125 Simplifying y = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.828427125, -1.828427125}
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