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Simplifying 4 + -4y + 4y2 = 64 Solving 4 + -4y + 4y2 = 64 Solving for variable 'y'. Reorder the terms: 4 + -64 + -4y + 4y2 = 64 + -64 Combine like terms: 4 + -64 = -60 -60 + -4y + 4y2 = 64 + -64 Combine like terms: 64 + -64 = 0 -60 + -4y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -1y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -1y + y2)' equal to zero and attempt to solve: Simplifying -15 + -1y + y2 = 0 Solving -15 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -1y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + -1y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1y + y2 = 0 + 15 -1y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1y + y2 = 15 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 15 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + -1y + y2 = 15.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (y + -0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
y + -0.5 = 3.905124838 Simplifying y + -0.5 = 3.905124838 Reorder the terms: -0.5 + y = 3.905124838 Solving -0.5 + y = 3.905124838 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 3.905124838 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 3.905124838 + 0.5 y = 3.905124838 + 0.5 Combine like terms: 3.905124838 + 0.5 = 4.405124838 y = 4.405124838 Simplifying y = 4.405124838Subproblem 2
y + -0.5 = -3.905124838 Simplifying y + -0.5 = -3.905124838 Reorder the terms: -0.5 + y = -3.905124838 Solving -0.5 + y = -3.905124838 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -3.905124838 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -3.905124838 + 0.5 y = -3.905124838 + 0.5 Combine like terms: -3.905124838 + 0.5 = -3.405124838 y = -3.405124838 Simplifying y = -3.405124838Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.405124838, -3.405124838}Solution
y = {4.405124838, -3.405124838}
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