y^2+-3y+-48=

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Solution for y^2+-3y+-48= equation:


Simplifying
y2 + -3y + -48 = 0

Reorder the terms:
-48 + -3y + y2 = 0

Solving
-48 + -3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -3y + 48 + y2 = 0 + 48

Reorder the terms:
-48 + 48 + -3y + y2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -3y + y2 = 0 + 48
-3y + y2 = 0 + 48

Combine like terms: 0 + 48 = 48
-3y + y2 = 48

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 48 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 48 + 2.25

Combine like terms: 48 + 2.25 = 50.25
2.25 + -3y + y2 = 50.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(y + -1.5) equal to 7.088723439 and -7.088723439.

Subproblem 1

y + -1.5 = 7.088723439 Simplifying y + -1.5 = 7.088723439 Reorder the terms: -1.5 + y = 7.088723439 Solving -1.5 + y = 7.088723439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 7.088723439 + 1.5 y = 7.088723439 + 1.5 Combine like terms: 7.088723439 + 1.5 = 8.588723439 y = 8.588723439 Simplifying y = 8.588723439

Subproblem 2

y + -1.5 = -7.088723439 Simplifying y + -1.5 = -7.088723439 Reorder the terms: -1.5 + y = -7.088723439 Solving -1.5 + y = -7.088723439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -7.088723439 + 1.5 y = -7.088723439 + 1.5 Combine like terms: -7.088723439 + 1.5 = -5.588723439 y = -5.588723439 Simplifying y = -5.588723439

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.588723439, -5.588723439}

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