x^2-4.9x+2.5=0

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Solution for x^2-4.9x+2.5=0 equation: 


Simplifying
x2 + -4.9x + 2.5 = 0

Reorder the terms:
2.5 + -4.9x + x2 = 0

Solving
2.5 + -4.9x + 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 + -4.9x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4.9x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4.9x + x2 = 0 + -2.5
-4.9x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4.9x + x2 = -2.5

The x term is -4.9x.  Take half its coefficient (-2.45).
Square it (6.0025) and add it to both sides.

Add '6.0025' to each side of the equation.
-4.9x + 6.0025 + x2 = -2.5 + 6.0025

Reorder the terms:
6.0025 + -4.9x + x2 = -2.5 + 6.0025

Combine like terms: -2.5 + 6.0025 = 3.5025
6.0025 + -4.9x + x2 = 3.5025

Factor a perfect square on the left side:
(x + -2.45)(x + -2.45) = 3.5025

Calculate the square root of the right side: 1.871496727

Break this problem into two subproblems by setting 
(x + -2.45) equal to 1.871496727 and -1.871496727.


Subproblem 1
x + -2.45 = 1.871496727

Simplifying
x + -2.45 = 1.871496727

Reorder the terms:
-2.45 + x = 1.871496727

Solving
-2.45 + x = 1.871496727

Solving for variable 'x'.

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

Add '2.45' to each side of the equation.
-2.45 + 2.45 + x = 1.871496727 + 2.45

Combine like terms: -2.45 + 2.45 = 0.00
0.00 + x = 1.871496727 + 2.45
x = 1.871496727 + 2.45

Combine like terms: 1.871496727 + 2.45 = 4.321496727
x = 4.321496727

Simplifying
x = 4.321496727


Subproblem 2
x + -2.45 = -1.871496727

Simplifying
x + -2.45 = -1.871496727

Reorder the terms:
-2.45 + x = -1.871496727

Solving
-2.45 + x = -1.871496727

Solving for variable 'x'.

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

Add '2.45' to each side of the equation.
-2.45 + 2.45 + x = -1.871496727 + 2.45

Combine like terms: -2.45 + 2.45 = 0.00
0.00 + x = -1.871496727 + 2.45
x = -1.871496727 + 2.45

Combine like terms: -1.871496727 + 2.45 = 0.578503273
x = 0.578503273

Simplifying
x = 0.578503273


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.321496727, 0.578503273}

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