x^2-1.6=-0.12x

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Solution for x^2-1.6=-0.12x equation:


Simplifying
x2 + -1.6 = -0.12x

Reorder the terms:
-1.6 + x2 = -0.12x

Solving
-1.6 + x2 = -0.12x

Solving for variable 'x'.

Reorder the terms:
-1.6 + 0.12x + x2 = -0.12x + 0.12x

Combine like terms: -0.12x + 0.12x = 0.00
-1.6 + 0.12x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.12x + 1.6 + x2 = 0.00 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.12x + x2 = 0.00 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.12x + x2 = 0.00 + 1.6
0.12x + x2 = 0.00 + 1.6

Combine like terms: 0.00 + 1.6 = 1.6
0.12x + x2 = 1.6

The x term is 0.12x.  Take half its coefficient (0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
0.12x + 0.0036 + x2 = 1.6 + 0.0036

Reorder the terms:
0.0036 + 0.12x + x2 = 1.6 + 0.0036

Combine like terms: 1.6 + 0.0036 = 1.6036
0.0036 + 0.12x + x2 = 1.6036

Factor a perfect square on the left side:
(x + 0.06)(x + 0.06) = 1.6036

Calculate the square root of the right side: 1.266333289

Break this problem into two subproblems by setting 
(x + 0.06) equal to 1.266333289 and -1.266333289.

Subproblem 1

x + 0.06 = 1.266333289 Simplifying x + 0.06 = 1.266333289 Reorder the terms: 0.06 + x = 1.266333289 Solving 0.06 + x = 1.266333289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 1.266333289 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 1.266333289 + -0.06 x = 1.266333289 + -0.06 Combine like terms: 1.266333289 + -0.06 = 1.206333289 x = 1.206333289 Simplifying x = 1.206333289

Subproblem 2

x + 0.06 = -1.266333289 Simplifying x + 0.06 = -1.266333289 Reorder the terms: 0.06 + x = -1.266333289 Solving 0.06 + x = -1.266333289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -1.266333289 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -1.266333289 + -0.06 x = -1.266333289 + -0.06 Combine like terms: -1.266333289 + -0.06 = -1.326333289 x = -1.326333289 Simplifying x = -1.326333289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.206333289, -1.326333289}

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