x^2-5.4x+7=0

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Solution for x^2-5.4x+7=0 equation: 


Simplifying
x2 + -5.4x + 7 = 0

Reorder the terms:
7 + -5.4x + x2 = 0

Solving
7 + -5.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -5.4x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -5.4x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5.4x + x2 = 0 + -7
-5.4x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-5.4x + x2 = -7

The x term is -5.4x.  Take half its coefficient (-2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
-5.4x + 7.29 + x2 = -7 + 7.29

Reorder the terms:
7.29 + -5.4x + x2 = -7 + 7.29

Combine like terms: -7 + 7.29 = 0.29
7.29 + -5.4x + x2 = 0.29

Factor a perfect square on the left side:
(x + -2.7)(x + -2.7) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(x + -2.7) equal to 0.538516481 and -0.538516481.


Subproblem 1
x + -2.7 = 0.538516481

Simplifying
x + -2.7 = 0.538516481

Reorder the terms:
-2.7 + x = 0.538516481

Solving
-2.7 + x = 0.538516481

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = 0.538516481 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = 0.538516481 + 2.7
x = 0.538516481 + 2.7

Combine like terms: 0.538516481 + 2.7 = 3.238516481
x = 3.238516481

Simplifying
x = 3.238516481


Subproblem 2
x + -2.7 = -0.538516481

Simplifying
x + -2.7 = -0.538516481

Reorder the terms:
-2.7 + x = -0.538516481

Solving
-2.7 + x = -0.538516481

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = -0.538516481 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = -0.538516481 + 2.7
x = -0.538516481 + 2.7

Combine like terms: -0.538516481 + 2.7 = 2.161483519
x = 2.161483519

Simplifying
x = 2.161483519


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.238516481, 2.161483519}

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