y^2+200y-3=0

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Solution for y^2+200y-3=0 equation:


Simplifying
y2 + 200y + -3 = 0

Reorder the terms:
-3 + 200y + y2 = 0

Solving
-3 + 200y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 200y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 200y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 200y + y2 = 0 + 3
200y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
200y + y2 = 3

The y term is 200y.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200y + 10000 + y2 = 3 + 10000

Reorder the terms:
10000 + 200y + y2 = 3 + 10000

Combine like terms: 3 + 10000 = 10003
10000 + 200y + y2 = 10003

Factor a perfect square on the left side:
(y + 100)(y + 100) = 10003

Calculate the square root of the right side: 100.014998875

Break this problem into two subproblems by setting 
(y + 100) equal to 100.014998875 and -100.014998875.

Subproblem 1

y + 100 = 100.014998875 Simplifying y + 100 = 100.014998875 Reorder the terms: 100 + y = 100.014998875 Solving 100 + y = 100.014998875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + y = 100.014998875 + -100 Combine like terms: 100 + -100 = 0 0 + y = 100.014998875 + -100 y = 100.014998875 + -100 Combine like terms: 100.014998875 + -100 = 0.014998875 y = 0.014998875 Simplifying y = 0.014998875

Subproblem 2

y + 100 = -100.014998875 Simplifying y + 100 = -100.014998875 Reorder the terms: 100 + y = -100.014998875 Solving 100 + y = -100.014998875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + y = -100.014998875 + -100 Combine like terms: 100 + -100 = 0 0 + y = -100.014998875 + -100 y = -100.014998875 + -100 Combine like terms: -100.014998875 + -100 = -200.014998875 y = -200.014998875 Simplifying y = -200.014998875

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.014998875, -200.014998875}

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