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Simplifying 4y2 + -24y + 4 = 0 Reorder the terms: 4 + -24y + 4y2 = 0 Solving 4 + -24y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -6y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -6y + y2)' equal to zero and attempt to solve: Simplifying 1 + -6y + y2 = 0 Solving 1 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -6y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6y + y2 = 0 + -1 -6y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6y + y2 = -1 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -1 + 9 Reorder the terms: 9 + -6y + y2 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + -6y + y2 = 8 Factor a perfect square on the left side: (y + -3)(y + -3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y + -3) equal to 2.828427125 and -2.828427125.Subproblem 1
y + -3 = 2.828427125 Simplifying y + -3 = 2.828427125 Reorder the terms: -3 + y = 2.828427125 Solving -3 + y = 2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.828427125 + 3 y = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 y = 5.828427125 Simplifying y = 5.828427125Subproblem 2
y + -3 = -2.828427125 Simplifying y + -3 = -2.828427125 Reorder the terms: -3 + y = -2.828427125 Solving -3 + y = -2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.828427125 + 3 y = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 y = 0.171572875 Simplifying y = 0.171572875Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.828427125, 0.171572875}Solution
y = {5.828427125, 0.171572875}
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