.04x^2+1.1x=100

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Solution for .04x^2+1.1x=100 equation:


Simplifying
0.04x2 + 1.1x = 100

Reorder the terms:
1.1x + 0.04x2 = 100

Solving
1.1x + 0.04x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 1.1x + 0.04x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 1.1x + 0.04x2 = 0

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

Divide each side by '0.04'.
-2500 + 27.5x + x2 = 0

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + 27.5x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + 27.5x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + 27.5x + x2 = 0 + 2500
27.5x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
27.5x + x2 = 2500

The x term is 27.5x.  Take half its coefficient (13.75).
Square it (189.0625) and add it to both sides.

Add '189.0625' to each side of the equation.
27.5x + 189.0625 + x2 = 2500 + 189.0625

Reorder the terms:
189.0625 + 27.5x + x2 = 2500 + 189.0625

Combine like terms: 2500 + 189.0625 = 2689.0625
189.0625 + 27.5x + x2 = 2689.0625

Factor a perfect square on the left side:
(x + 13.75)(x + 13.75) = 2689.0625

Calculate the square root of the right side: 51.856171282

Break this problem into two subproblems by setting 
(x + 13.75) equal to 51.856171282 and -51.856171282.

Subproblem 1

x + 13.75 = 51.856171282 Simplifying x + 13.75 = 51.856171282 Reorder the terms: 13.75 + x = 51.856171282 Solving 13.75 + x = 51.856171282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 51.856171282 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 51.856171282 + -13.75 x = 51.856171282 + -13.75 Combine like terms: 51.856171282 + -13.75 = 38.106171282 x = 38.106171282 Simplifying x = 38.106171282

Subproblem 2

x + 13.75 = -51.856171282 Simplifying x + 13.75 = -51.856171282 Reorder the terms: 13.75 + x = -51.856171282 Solving 13.75 + x = -51.856171282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -51.856171282 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -51.856171282 + -13.75 x = -51.856171282 + -13.75 Combine like terms: -51.856171282 + -13.75 = -65.606171282 x = -65.606171282 Simplifying x = -65.606171282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {38.106171282, -65.606171282}

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