x^2-4.7x+2.5=0

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Solution for x^2-4.7x+2.5=0 equation: 


Simplifying
x2 + -4.7x + 2.5 = 0

Reorder the terms:
2.5 + -4.7x + x2 = 0

Solving
2.5 + -4.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4.7x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4.7x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4.7x + x2 = 0 + -2.5
-4.7x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4.7x + x2 = -2.5

The x term is -4.7x.  Take half its coefficient (-2.35).
Square it (5.5225) and add it to both sides.

Add '5.5225' to each side of the equation.
-4.7x + 5.5225 + x2 = -2.5 + 5.5225

Reorder the terms:
5.5225 + -4.7x + x2 = -2.5 + 5.5225

Combine like terms: -2.5 + 5.5225 = 3.0225
5.5225 + -4.7x + x2 = 3.0225

Factor a perfect square on the left side:
(x + -2.35)(x + -2.35) = 3.0225

Calculate the square root of the right side: 1.738533865

Break this problem into two subproblems by setting 
(x + -2.35) equal to 1.738533865 and -1.738533865.


Subproblem 1
x + -2.35 = 1.738533865

Simplifying
x + -2.35 = 1.738533865

Reorder the terms:
-2.35 + x = 1.738533865

Solving
-2.35 + x = 1.738533865

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = 1.738533865 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = 1.738533865 + 2.35
x = 1.738533865 + 2.35

Combine like terms: 1.738533865 + 2.35 = 4.088533865
x = 4.088533865

Simplifying
x = 4.088533865


Subproblem 2
x + -2.35 = -1.738533865

Simplifying
x + -2.35 = -1.738533865

Reorder the terms:
-2.35 + x = -1.738533865

Solving
-2.35 + x = -1.738533865

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = -1.738533865 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = -1.738533865 + 2.35
x = -1.738533865 + 2.35

Combine like terms: -1.738533865 + 2.35 = 0.611466135
x = 0.611466135

Simplifying
x = 0.611466135


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.088533865, 0.611466135}

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