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Simplifying -25y2 + 100y + 100 = 0 Reorder the terms: 100 + 100y + -25y2 = 0 Solving 100 + 100y + -25y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '25'. 25(4 + 4y + -1y2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(4 + 4y + -1y2)' equal to zero and attempt to solve: Simplifying 4 + 4y + -1y2 = 0 Solving 4 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -4y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4y + y2 = 0 + 4 -4y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4y + y2 = 4 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 4 + 4 Reorder the terms: 4 + -4y + y2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4y + y2 = 8 Factor a perfect square on the left side: (y + -2)(y + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
y + -2 = 2.828427125 Simplifying y + -2 = 2.828427125 Reorder the terms: -2 + y = 2.828427125 Solving -2 + y = 2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.828427125 + 2 y = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 y = 4.828427125 Simplifying y = 4.828427125Subproblem 2
y + -2 = -2.828427125 Simplifying y + -2 = -2.828427125 Reorder the terms: -2 + y = -2.828427125 Solving -2 + y = -2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.828427125 + 2 y = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 y = -0.828427125 Simplifying y = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.828427125, -0.828427125}Solution
y = {4.828427125, -0.828427125}
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