.4x^2-40x+360=0

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Solution for .4x^2-40x+360=0 equation:


Simplifying
0.4x2 + -40x + 360 = 0

Reorder the terms:
360 + -40x + 0.4x2 = 0

Solving
360 + -40x + 0.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.4'.
900 + -100x + x2 = 0

Move the constant term to the right:

Add '-900' to each side of the equation.
900 + -100x + -900 + x2 = 0 + -900

Reorder the terms:
900 + -900 + -100x + x2 = 0 + -900

Combine like terms: 900 + -900 = 0
0 + -100x + x2 = 0 + -900
-100x + x2 = 0 + -900

Combine like terms: 0 + -900 = -900
-100x + x2 = -900

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -900 + 2500

Reorder the terms:
2500 + -100x + x2 = -900 + 2500

Combine like terms: -900 + 2500 = 1600
2500 + -100x + x2 = 1600

Factor a perfect square on the left side:
(x + -50)(x + -50) = 1600

Calculate the square root of the right side: 40

Break this problem into two subproblems by setting 
(x + -50) equal to 40 and -40.

Subproblem 1

x + -50 = 40 Simplifying x + -50 = 40 Reorder the terms: -50 + x = 40 Solving -50 + x = 40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 40 + 50 Combine like terms: -50 + 50 = 0 0 + x = 40 + 50 x = 40 + 50 Combine like terms: 40 + 50 = 90 x = 90 Simplifying x = 90

Subproblem 2

x + -50 = -40 Simplifying x + -50 = -40 Reorder the terms: -50 + x = -40 Solving -50 + x = -40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -40 + 50 Combine like terms: -50 + 50 = 0 0 + x = -40 + 50 x = -40 + 50 Combine like terms: -40 + 50 = 10 x = 10 Simplifying x = 10

Solution

The solution to the problem is based on the solutions from the subproblems. x = {90, 10}

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