y^2-6.5y+.64=0

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Solution for y^2-6.5y+.64=0 equation:


Simplifying
y2 + -6.5y + 0.64 = 0

Reorder the terms:
0.64 + -6.5y + y2 = 0

Solving
0.64 + -6.5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-0.64' to each side of the equation.
0.64 + -6.5y + -0.64 + y2 = 0 + -0.64

Reorder the terms:
0.64 + -0.64 + -6.5y + y2 = 0 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
0.00 + -6.5y + y2 = 0 + -0.64
-6.5y + y2 = 0 + -0.64

Combine like terms: 0 + -0.64 = -0.64
-6.5y + y2 = -0.64

The y term is -6.5y.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5y + 10.5625 + y2 = -0.64 + 10.5625

Reorder the terms:
10.5625 + -6.5y + y2 = -0.64 + 10.5625

Combine like terms: -0.64 + 10.5625 = 9.9225
10.5625 + -6.5y + y2 = 9.9225

Factor a perfect square on the left side:
(y + -3.25)(y + -3.25) = 9.9225

Calculate the square root of the right side: 3.15

Break this problem into two subproblems by setting 
(y + -3.25) equal to 3.15 and -3.15.

Subproblem 1

y + -3.25 = 3.15 Simplifying y + -3.25 = 3.15 Reorder the terms: -3.25 + y = 3.15 Solving -3.25 + y = 3.15 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = 3.15 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = 3.15 + 3.25 y = 3.15 + 3.25 Combine like terms: 3.15 + 3.25 = 6.4 y = 6.4 Simplifying y = 6.4

Subproblem 2

y + -3.25 = -3.15 Simplifying y + -3.25 = -3.15 Reorder the terms: -3.25 + y = -3.15 Solving -3.25 + y = -3.15 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = -3.15 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = -3.15 + 3.25 y = -3.15 + 3.25 Combine like terms: -3.15 + 3.25 = 0.1 y = 0.1 Simplifying y = 0.1

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.4, 0.1}

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