-.8x^2+5.8x-5.4=0

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Solution for -.8x^2+5.8x-5.4=0 equation:


Simplifying
-0.8x2 + 5.8x + -5.4 = 0

Reorder the terms:
-5.4 + 5.8x + -0.8x2 = 0

Solving
-5.4 + 5.8x + -0.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
6.75 + -7.25x + x2 = 0

Move the constant term to the right:

Add '-6.75' to each side of the equation.
6.75 + -7.25x + -6.75 + x2 = 0 + -6.75

Reorder the terms:
6.75 + -6.75 + -7.25x + x2 = 0 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + -7.25x + x2 = 0 + -6.75
-7.25x + x2 = 0 + -6.75

Combine like terms: 0 + -6.75 = -6.75
-7.25x + x2 = -6.75

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = -6.75 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = -6.75 + 13.140625

Combine like terms: -6.75 + 13.140625 = 6.390625
13.140625 + -7.25x + x2 = 6.390625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 6.390625

Calculate the square root of the right side: 2.527968552

Break this problem into two subproblems by setting 
(x + -3.625) equal to 2.527968552 and -2.527968552.


Subproblem 1
x + -3.625 = 2.527968552

Simplifying
x + -3.625 = 2.527968552

Reorder the terms:
-3.625 + x = 2.527968552

Solving
-3.625 + x = 2.527968552

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = 2.527968552 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = 2.527968552 + 3.625
x = 2.527968552 + 3.625

Combine like terms: 2.527968552 + 3.625 = 6.152968552
x = 6.152968552

Simplifying
x = 6.152968552


Subproblem 2
x + -3.625 = -2.527968552

Simplifying
x + -3.625 = -2.527968552

Reorder the terms:
-3.625 + x = -2.527968552

Solving
-3.625 + x = -2.527968552

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = -2.527968552 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = -2.527968552 + 3.625
x = -2.527968552 + 3.625

Combine like terms: -2.527968552 + 3.625 = 1.097031448
x = 1.097031448

Simplifying
x = 1.097031448


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.152968552, 1.097031448}

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