y^2=y+100

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Solution for y^2=y+100 equation:


Simplifying
y2 = y + 100

Reorder the terms:
y2 = 100 + y

Solving
y2 = 100 + y

Solving for variable 'y'.

Reorder the terms:
-100 + -1y + y2 = 100 + y + -100 + -1y

Reorder the terms:
-100 + -1y + y2 = 100 + -100 + y + -1y

Combine like terms: 100 + -100 = 0
-100 + -1y + y2 = 0 + y + -1y
-100 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-100 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -1y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + -1y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1y + y2 = 0 + 100
-1y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
-1y + y2 = 100

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 100 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + -1y + y2 = 100.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(y + -0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

y + -0.5 = 10.012492197 Simplifying y + -0.5 = 10.012492197 Reorder the terms: -0.5 + y = 10.012492197 Solving -0.5 + y = 10.012492197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 10.012492197 + 0.5 y = 10.012492197 + 0.5 Combine like terms: 10.012492197 + 0.5 = 10.512492197 y = 10.512492197 Simplifying y = 10.512492197

Subproblem 2

y + -0.5 = -10.012492197 Simplifying y + -0.5 = -10.012492197 Reorder the terms: -0.5 + y = -10.012492197 Solving -0.5 + y = -10.012492197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -10.012492197 + 0.5 y = -10.012492197 + 0.5 Combine like terms: -10.012492197 + 0.5 = -9.512492197 y = -9.512492197 Simplifying y = -9.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. y = {10.512492197, -9.512492197}

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