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Simplifying 4y2 + -20y + -50 = 0 Reorder the terms: -50 + -20y + 4y2 = 0 Solving -50 + -20y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -10y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -10y + 2y2)' equal to zero and attempt to solve: Simplifying -25 + -10y + 2y2 = 0 Solving -25 + -10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -5y + y2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -5y + 12.5 + y2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -5y + y2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -5y + y2 = 0 + 12.5 -5y + y2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -5y + y2 = 12.5 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 12.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 12.5 + 6.25 Combine like terms: 12.5 + 6.25 = 18.75 6.25 + -5y + y2 = 18.75 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (y + -2.5) equal to 4.330127019 and -4.330127019.Subproblem 1
y + -2.5 = 4.330127019 Simplifying y + -2.5 = 4.330127019 Reorder the terms: -2.5 + y = 4.330127019 Solving -2.5 + y = 4.330127019 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 4.330127019 + 2.5 y = 4.330127019 + 2.5 Combine like terms: 4.330127019 + 2.5 = 6.830127019 y = 6.830127019 Simplifying y = 6.830127019Subproblem 2
y + -2.5 = -4.330127019 Simplifying y + -2.5 = -4.330127019 Reorder the terms: -2.5 + y = -4.330127019 Solving -2.5 + y = -4.330127019 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -4.330127019 + 2.5 y = -4.330127019 + 2.5 Combine like terms: -4.330127019 + 2.5 = -1.830127019 y = -1.830127019 Simplifying y = -1.830127019Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.830127019, -1.830127019}Solution
y = {6.830127019, -1.830127019}
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