x^2-4.9x=2.7

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Solution for x^2-4.9x=2.7 equation: 


Simplifying
x2 + -4.9x = 2.7

Reorder the terms:
-4.9x + x2 = 2.7

Solving
-4.9x + x2 = 2.7

Solving for variable 'x'.

Reorder the terms:
-2.7 + -4.9x + x2 = 2.7 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
-2.7 + -4.9x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.7' to each side of the equation.
-2.7 + -4.9x + 2.7 + x2 = 0.0 + 2.7

Reorder the terms:
-2.7 + 2.7 + -4.9x + x2 = 0.0 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + -4.9x + x2 = 0.0 + 2.7
-4.9x + x2 = 0.0 + 2.7

Combine like terms: 0.0 + 2.7 = 2.7
-4.9x + x2 = 2.7

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 = 2.7 + 6.0025

Reorder the terms:
6.0025 + -4.9x + x2 = 2.7 + 6.0025

Combine like terms: 2.7 + 6.0025 = 8.7025
6.0025 + -4.9x + x2 = 8.7025

Factor a perfect square on the left side:
(x + -2.45)(x + -2.45) = 8.7025

Calculate the square root of the right side: 2.95

Break this problem into two subproblems by setting 
(x + -2.45) equal to 2.95 and -2.95.


Subproblem 1
x + -2.45 = 2.95

Simplifying
x + -2.45 = 2.95

Reorder the terms:
-2.45 + x = 2.95

Solving
-2.45 + x = 2.95

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 = 2.95 + 2.45

Combine like terms: -2.45 + 2.45 = 0.00
0.00 + x = 2.95 + 2.45
x = 2.95 + 2.45

Combine like terms: 2.95 + 2.45 = 5.4
x = 5.4

Simplifying
x = 5.4


Subproblem 2
x + -2.45 = -2.95

Simplifying
x + -2.45 = -2.95

Reorder the terms:
-2.45 + x = -2.95

Solving
-2.45 + x = -2.95

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 = -2.95 + 2.45

Combine like terms: -2.45 + 2.45 = 0.00
0.00 + x = -2.95 + 2.45
x = -2.95 + 2.45

Combine like terms: -2.95 + 2.45 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.4, -0.5}

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