1=y(8y-4)

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Solution for 1=y(8y-4) equation:


Simplifying
1 = y(8y + -4)

Reorder the terms:
1 = y(-4 + 8y)
1 = (-4 * y + 8y * y)
1 = (-4y + 8y2)

Solving
1 = -4y + 8y2

Solving for variable 'y'.

Reorder the terms:
1 + 4y + -8y2 = -4y + 4y + 8y2 + -8y2

Combine like terms: -4y + 4y = 0
1 + 4y + -8y2 = 0 + 8y2 + -8y2
1 + 4y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
1 + 4y + -8y2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.125 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.5y + 0.125 + y2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.5y + y2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.5y + y2 = 0 + 0.125
-0.5y + y2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.5y + y2 = 0.125

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.125 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.125 + 0.0625

Combine like terms: 0.125 + 0.0625 = 0.1875
0.0625 + -0.5y + y2 = 0.1875

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.1875

Calculate the square root of the right side: 0.433012702

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.433012702 and -0.433012702.

Subproblem 1

y + -0.25 = 0.433012702 Simplifying y + -0.25 = 0.433012702 Reorder the terms: -0.25 + y = 0.433012702 Solving -0.25 + y = 0.433012702 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 0.433012702 + 0.25 y = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 y = 0.683012702 Simplifying y = 0.683012702

Subproblem 2

y + -0.25 = -0.433012702 Simplifying y + -0.25 = -0.433012702 Reorder the terms: -0.25 + y = -0.433012702 Solving -0.25 + y = -0.433012702 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -0.433012702 + 0.25 y = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 y = -0.183012702 Simplifying y = -0.183012702

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.683012702, -0.183012702}

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