y^2-9y-6=0

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Solution for y^2-9y-6=0 equation:


Simplifying
y2 + -9y + -6 = 0

Reorder the terms:
-6 + -9y + y2 = 0

Solving
-6 + -9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -9y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + -9y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -9y + y2 = 0 + 6
-9y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
-9y + y2 = 6

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = 6 + 20.25

Reorder the terms:
20.25 + -9y + y2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + -9y + y2 = 26.25

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(y + -4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

y + -4.5 = 5.123475383 Simplifying y + -4.5 = 5.123475383 Reorder the terms: -4.5 + y = 5.123475383 Solving -4.5 + y = 5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 5.123475383 + 4.5 y = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 y = 9.623475383 Simplifying y = 9.623475383

Subproblem 2

y + -4.5 = -5.123475383 Simplifying y + -4.5 = -5.123475383 Reorder the terms: -4.5 + y = -5.123475383 Solving -4.5 + y = -5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -5.123475383 + 4.5 y = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 y = -0.623475383 Simplifying y = -0.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.623475383, -0.623475383}

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