2y^2+40-210y=0

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Solution for 2y^2+40-210y=0 equation:


Simplifying
2y2 + 40 + -210y = 0

Reorder the terms:
40 + -210y + 2y2 = 0

Solving
40 + -210y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -105y + y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(20 + -105y + y2)' equal to zero and attempt to solve: Simplifying 20 + -105y + y2 = 0 Solving 20 + -105y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -105y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + -105y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -105y + y2 = 0 + -20 -105y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 -105y + y2 = -20 The y term is -105y. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105y + 2756.25 + y2 = -20 + 2756.25 Reorder the terms: 2756.25 + -105y + y2 = -20 + 2756.25 Combine like terms: -20 + 2756.25 = 2736.25 2756.25 + -105y + y2 = 2736.25 Factor a perfect square on the left side: (y + -52.5)(y + -52.5) = 2736.25 Calculate the square root of the right side: 52.309177015 Break this problem into two subproblems by setting (y + -52.5) equal to 52.309177015 and -52.309177015.

Subproblem 1

y + -52.5 = 52.309177015 Simplifying y + -52.5 = 52.309177015 Reorder the terms: -52.5 + y = 52.309177015 Solving -52.5 + y = 52.309177015 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + y = 52.309177015 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + y = 52.309177015 + 52.5 y = 52.309177015 + 52.5 Combine like terms: 52.309177015 + 52.5 = 104.809177015 y = 104.809177015 Simplifying y = 104.809177015

Subproblem 2

y + -52.5 = -52.309177015 Simplifying y + -52.5 = -52.309177015 Reorder the terms: -52.5 + y = -52.309177015 Solving -52.5 + y = -52.309177015 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + y = -52.309177015 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + y = -52.309177015 + 52.5 y = -52.309177015 + 52.5 Combine like terms: -52.309177015 + 52.5 = 0.190822985 y = 0.190822985 Simplifying y = 0.190822985

Solution

The solution to the problem is based on the solutions from the subproblems. y = {104.809177015, 0.190822985}

Solution

y = {104.809177015, 0.190822985}

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