10y^2=26y+16

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Solution for 10y^2=26y+16 equation:


Simplifying
10y2 = 26y + 16

Reorder the terms:
10y2 = 16 + 26y

Solving
10y2 = 16 + 26y

Solving for variable 'y'.

Reorder the terms:
-16 + -26y + 10y2 = 16 + 26y + -16 + -26y

Reorder the terms:
-16 + -26y + 10y2 = 16 + -16 + 26y + -26y

Combine like terms: 16 + -16 = 0
-16 + -26y + 10y2 = 0 + 26y + -26y
-16 + -26y + 10y2 = 26y + -26y

Combine like terms: 26y + -26y = 0
-16 + -26y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -13y + 5y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-8 + -13y + 5y2)' equal to zero and attempt to solve: Simplifying -8 + -13y + 5y2 = 0 Solving -8 + -13y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -2.6y + y2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -2.6y + 1.6 + y2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -2.6y + y2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -2.6y + y2 = 0 + 1.6 -2.6y + y2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -2.6y + y2 = 1.6 The y term is -2.6y. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6y + 1.69 + y2 = 1.6 + 1.69 Reorder the terms: 1.69 + -2.6y + y2 = 1.6 + 1.69 Combine like terms: 1.6 + 1.69 = 3.29 1.69 + -2.6y + y2 = 3.29 Factor a perfect square on the left side: (y + -1.3)(y + -1.3) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (y + -1.3) equal to 1.813835715 and -1.813835715.

Subproblem 1

y + -1.3 = 1.813835715 Simplifying y + -1.3 = 1.813835715 Reorder the terms: -1.3 + y = 1.813835715 Solving -1.3 + y = 1.813835715 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = 1.813835715 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = 1.813835715 + 1.3 y = 1.813835715 + 1.3 Combine like terms: 1.813835715 + 1.3 = 3.113835715 y = 3.113835715 Simplifying y = 3.113835715

Subproblem 2

y + -1.3 = -1.813835715 Simplifying y + -1.3 = -1.813835715 Reorder the terms: -1.3 + y = -1.813835715 Solving -1.3 + y = -1.813835715 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = -1.813835715 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = -1.813835715 + 1.3 y = -1.813835715 + 1.3 Combine like terms: -1.813835715 + 1.3 = -0.513835715 y = -0.513835715 Simplifying y = -0.513835715

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.113835715, -0.513835715}

Solution

y = {3.113835715, -0.513835715}

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