1.98-y^2-4y=0

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Solution for 1.98-y^2-4y=0 equation:


Simplifying
1.98 + -1y2 + -4y = 0

Reorder the terms:
1.98 + -4y + -1y2 = 0

Solving
1.98 + -4y + -1y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1.98 + 4y + y2 = 0

Move the constant term to the right:

Add '1.98' to each side of the equation.
-1.98 + 4y + 1.98 + y2 = 0 + 1.98

Reorder the terms:
-1.98 + 1.98 + 4y + y2 = 0 + 1.98

Combine like terms: -1.98 + 1.98 = 0.00
0.00 + 4y + y2 = 0 + 1.98
4y + y2 = 0 + 1.98

Combine like terms: 0 + 1.98 = 1.98
4y + y2 = 1.98

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 1.98 + 4

Reorder the terms:
4 + 4y + y2 = 1.98 + 4

Combine like terms: 1.98 + 4 = 5.98
4 + 4y + y2 = 5.98

Factor a perfect square on the left side:
(y + 2)(y + 2) = 5.98

Calculate the square root of the right side: 2.445403852

Break this problem into two subproblems by setting 
(y + 2) equal to 2.445403852 and -2.445403852.

Subproblem 1

y + 2 = 2.445403852 Simplifying y + 2 = 2.445403852 Reorder the terms: 2 + y = 2.445403852 Solving 2 + y = 2.445403852 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.445403852 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.445403852 + -2 y = 2.445403852 + -2 Combine like terms: 2.445403852 + -2 = 0.445403852 y = 0.445403852 Simplifying y = 0.445403852

Subproblem 2

y + 2 = -2.445403852 Simplifying y + 2 = -2.445403852 Reorder the terms: 2 + y = -2.445403852 Solving 2 + y = -2.445403852 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.445403852 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.445403852 + -2 y = -2.445403852 + -2 Combine like terms: -2.445403852 + -2 = -4.445403852 y = -4.445403852 Simplifying y = -4.445403852

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.445403852, -4.445403852}

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