-.1x^2+27x-400=0

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Solution for -.1x^2+27x-400=0 equation: 


Simplifying
-0.1x2 + 27x + -400 = 0

Reorder the terms:
-400 + 27x + -0.1x2 = 0

Solving
-400 + 27x + -0.1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
4000 + -270x + x2 = 0

Move the constant term to the right:

Add '-4000' to each side of the equation.
4000 + -270x + -4000 + x2 = 0 + -4000

Reorder the terms:
4000 + -4000 + -270x + x2 = 0 + -4000

Combine like terms: 4000 + -4000 = 0
0 + -270x + x2 = 0 + -4000
-270x + x2 = 0 + -4000

Combine like terms: 0 + -4000 = -4000
-270x + x2 = -4000

The x term is -270x.  Take half its coefficient (-135).
Square it (18225) and add it to both sides.

Add '18225' to each side of the equation.
-270x + 18225 + x2 = -4000 + 18225

Reorder the terms:
18225 + -270x + x2 = -4000 + 18225

Combine like terms: -4000 + 18225 = 14225
18225 + -270x + x2 = 14225

Factor a perfect square on the left side:
(x + -135)(x + -135) = 14225

Calculate the square root of the right side: 119.268604419

Break this problem into two subproblems by setting 
(x + -135) equal to 119.268604419 and -119.268604419.


Subproblem 1
x + -135 = 119.268604419

Simplifying
x + -135 = 119.268604419

Reorder the terms:
-135 + x = 119.268604419

Solving
-135 + x = 119.268604419

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '135' to each side of the equation.
-135 + 135 + x = 119.268604419 + 135

Combine like terms: -135 + 135 = 0
0 + x = 119.268604419 + 135
x = 119.268604419 + 135

Combine like terms: 119.268604419 + 135 = 254.268604419
x = 254.268604419

Simplifying
x = 254.268604419


Subproblem 2
x + -135 = -119.268604419

Simplifying
x + -135 = -119.268604419

Reorder the terms:
-135 + x = -119.268604419

Solving
-135 + x = -119.268604419

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '135' to each side of the equation.
-135 + 135 + x = -119.268604419 + 135

Combine like terms: -135 + 135 = 0
0 + x = -119.268604419 + 135
x = -119.268604419 + 135

Combine like terms: -119.268604419 + 135 = 15.731395581
x = 15.731395581

Simplifying
x = 15.731395581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {254.268604419, 15.731395581}

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