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Simplifying 4 + 4y + 2y2 = 64 Solving 4 + 4y + 2y2 = 64 Solving for variable 'y'. Reorder the terms: 4 + -64 + 4y + 2y2 = 64 + -64 Combine like terms: 4 + -64 = -60 -60 + 4y + 2y2 = 64 + -64 Combine like terms: 64 + -64 = 0 -60 + 4y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 2y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 2y + y2)' equal to zero and attempt to solve: Simplifying -30 + 2y + y2 = 0 Solving -30 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 2y + 30 + y2 = 0 + 30 Reorder the terms: -30 + 30 + 2y + y2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2y + y2 = 0 + 30 2y + y2 = 0 + 30 Combine like terms: 0 + 30 = 30 2y + y2 = 30 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 = 30 + 1 Reorder the terms: 1 + 2y + y2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2y + y2 = 31 Factor a perfect square on the left side: (y + 1)(y + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (y + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
y + 1 = 5.567764363 Simplifying y + 1 = 5.567764363 Reorder the terms: 1 + y = 5.567764363 Solving 1 + y = 5.567764363 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 = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + y = 5.567764363 + -1 y = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 y = 4.567764363 Simplifying y = 4.567764363Subproblem 2
y + 1 = -5.567764363 Simplifying y + 1 = -5.567764363 Reorder the terms: 1 + y = -5.567764363 Solving 1 + y = -5.567764363 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 = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + y = -5.567764363 + -1 y = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 y = -6.567764363 Simplifying y = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.567764363, -6.567764363}Solution
y = {4.567764363, -6.567764363}
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