5y(2y-10)=25

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Solution for 5y(2y-10)=25 equation:


Simplifying
5y(2y + -10) = 25

Reorder the terms:
5y(-10 + 2y) = 25
(-10 * 5y + 2y * 5y) = 25
(-50y + 10y2) = 25

Solving
-50y + 10y2 = 25

Solving for variable 'y'.

Reorder the terms:
-25 + -50y + 10y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -50y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -10y + 2y2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-5 + -10y + 2y2)' equal to zero and attempt to solve: Simplifying -5 + -10y + 2y2 = 0 Solving -5 + -10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5y + y2 = 0 + 2.5 -5y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5y + y2 = 2.5 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 = 2.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5y + y2 = 8.75 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (y + -2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

y + -2.5 = 2.958039892 Simplifying y + -2.5 = 2.958039892 Reorder the terms: -2.5 + y = 2.958039892 Solving -2.5 + y = 2.958039892 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 = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.958039892 + 2.5 y = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 y = 5.458039892 Simplifying y = 5.458039892

Subproblem 2

y + -2.5 = -2.958039892 Simplifying y + -2.5 = -2.958039892 Reorder the terms: -2.5 + y = -2.958039892 Solving -2.5 + y = -2.958039892 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 = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.958039892 + 2.5 y = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 y = -0.458039892 Simplifying y = -0.458039892

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.458039892, -0.458039892}

Solution

y = {5.458039892, -0.458039892}

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