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Simplifying 2y2 + 20y + -50 = 0 Reorder the terms: -50 + 20y + 2y2 = 0 Solving -50 + 20y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 10y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 10y + y2)' equal to zero and attempt to solve: Simplifying -25 + 10y + y2 = 0 Solving -25 + 10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 10y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + 10y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 10y + y2 = 0 + 25 10y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 10y + y2 = 25 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 25 + 25 Reorder the terms: 25 + 10y + y2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + 10y + y2 = 50 Factor a perfect square on the left side: (y + 5)(y + 5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (y + 5) equal to 7.071067812 and -7.071067812.Subproblem 1
y + 5 = 7.071067812 Simplifying y + 5 = 7.071067812 Reorder the terms: 5 + y = 7.071067812 Solving 5 + y = 7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + y = 7.071067812 + -5 y = 7.071067812 + -5 Combine like terms: 7.071067812 + -5 = 2.071067812 y = 2.071067812 Simplifying y = 2.071067812Subproblem 2
y + 5 = -7.071067812 Simplifying y + 5 = -7.071067812 Reorder the terms: 5 + y = -7.071067812 Solving 5 + y = -7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + y = -7.071067812 + -5 y = -7.071067812 + -5 Combine like terms: -7.071067812 + -5 = -12.071067812 y = -12.071067812 Simplifying y = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.071067812, -12.071067812}Solution
y = {2.071067812, -12.071067812}
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