y^2-19y+77=

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Solution for y^2-19y+77= equation:


Simplifying
y2 + -19y + 77 = 0

Reorder the terms:
77 + -19y + y2 = 0

Solving
77 + -19y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-77' to each side of the equation.
77 + -19y + -77 + y2 = 0 + -77

Reorder the terms:
77 + -77 + -19y + y2 = 0 + -77

Combine like terms: 77 + -77 = 0
0 + -19y + y2 = 0 + -77
-19y + y2 = 0 + -77

Combine like terms: 0 + -77 = -77
-19y + y2 = -77

The y term is -19y.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19y + 90.25 + y2 = -77 + 90.25

Reorder the terms:
90.25 + -19y + y2 = -77 + 90.25

Combine like terms: -77 + 90.25 = 13.25
90.25 + -19y + y2 = 13.25

Factor a perfect square on the left side:
(y + -9.5)(y + -9.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(y + -9.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

y + -9.5 = 3.640054945 Simplifying y + -9.5 = 3.640054945 Reorder the terms: -9.5 + y = 3.640054945 Solving -9.5 + y = 3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 3.640054945 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 3.640054945 + 9.5 y = 3.640054945 + 9.5 Combine like terms: 3.640054945 + 9.5 = 13.140054945 y = 13.140054945 Simplifying y = 13.140054945

Subproblem 2

y + -9.5 = -3.640054945 Simplifying y + -9.5 = -3.640054945 Reorder the terms: -9.5 + y = -3.640054945 Solving -9.5 + y = -3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -3.640054945 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -3.640054945 + 9.5 y = -3.640054945 + 9.5 Combine like terms: -3.640054945 + 9.5 = 5.859945055 y = 5.859945055 Simplifying y = 5.859945055

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.140054945, 5.859945055}

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