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Simplifying -64 + y2 + 2y = 4y Reorder the terms: -64 + 2y + y2 = 4y Solving -64 + 2y + y2 = 4y Solving for variable 'y'. Reorder the terms: -64 + 2y + -4y + y2 = 4y + -4y Combine like terms: 2y + -4y = -2y -64 + -2y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -64 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -2y + 64 + y2 = 0 + 64 Reorder the terms: -64 + 64 + -2y + y2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -2y + y2 = 0 + 64 -2y + y2 = 0 + 64 Combine like terms: 0 + 64 = 64 -2y + y2 = 64 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 = 64 + 1 Reorder the terms: 1 + -2y + y2 = 64 + 1 Combine like terms: 64 + 1 = 65 1 + -2y + y2 = 65 Factor a perfect square on the left side: (y + -1)(y + -1) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (y + -1) equal to 8.062257748 and -8.062257748.Subproblem 1
y + -1 = 8.062257748 Simplifying y + -1 = 8.062257748 Reorder the terms: -1 + y = 8.062257748 Solving -1 + y = 8.062257748 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 = 8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + y = 8.062257748 + 1 y = 8.062257748 + 1 Combine like terms: 8.062257748 + 1 = 9.062257748 y = 9.062257748 Simplifying y = 9.062257748Subproblem 2
y + -1 = -8.062257748 Simplifying y + -1 = -8.062257748 Reorder the terms: -1 + y = -8.062257748 Solving -1 + y = -8.062257748 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 = -8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + y = -8.062257748 + 1 y = -8.062257748 + 1 Combine like terms: -8.062257748 + 1 = -7.062257748 y = -7.062257748 Simplifying y = -7.062257748Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.062257748, -7.062257748}
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