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Simplifying 2y2 + 10y = 84 Reorder the terms: 10y + 2y2 = 84 Solving 10y + 2y2 = 84 Solving for variable 'y'. Reorder the terms: -84 + 10y + 2y2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 10y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 5y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 5y + y2)' equal to zero and attempt to solve: Simplifying -42 + 5y + y2 = 0 Solving -42 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 5y + 42 + y2 = 0 + 42 Reorder the terms: -42 + 42 + 5y + y2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 5y + y2 = 0 + 42 5y + y2 = 0 + 42 Combine like terms: 0 + 42 = 42 5y + y2 = 42 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 = 42 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 42 + 6.25 Combine like terms: 42 + 6.25 = 48.25 6.25 + 5y + y2 = 48.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (y + 2.5) equal to 6.946221995 and -6.946221995.Subproblem 1
y + 2.5 = 6.946221995 Simplifying y + 2.5 = 6.946221995 Reorder the terms: 2.5 + y = 6.946221995 Solving 2.5 + y = 6.946221995 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 = 6.946221995 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 6.946221995 + -2.5 y = 6.946221995 + -2.5 Combine like terms: 6.946221995 + -2.5 = 4.446221995 y = 4.446221995 Simplifying y = 4.446221995Subproblem 2
y + 2.5 = -6.946221995 Simplifying y + 2.5 = -6.946221995 Reorder the terms: 2.5 + y = -6.946221995 Solving 2.5 + y = -6.946221995 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 = -6.946221995 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -6.946221995 + -2.5 y = -6.946221995 + -2.5 Combine like terms: -6.946221995 + -2.5 = -9.446221995 y = -9.446221995 Simplifying y = -9.446221995Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.446221995, -9.446221995}Solution
y = {4.446221995, -9.446221995}
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