x^2-2.8x-3.7=0

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Solution for x^2-2.8x-3.7=0 equation:


Simplifying
x2 + -2.8x + -3.7 = 0

Reorder the terms:
-3.7 + -2.8x + x2 = 0

Solving
-3.7 + -2.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3.7' to each side of the equation.
-3.7 + -2.8x + 3.7 + x2 = 0 + 3.7

Reorder the terms:
-3.7 + 3.7 + -2.8x + x2 = 0 + 3.7

Combine like terms: -3.7 + 3.7 = 0.0
0.0 + -2.8x + x2 = 0 + 3.7
-2.8x + x2 = 0 + 3.7

Combine like terms: 0 + 3.7 = 3.7
-2.8x + x2 = 3.7

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = 3.7 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 3.7 + 1.96

Combine like terms: 3.7 + 1.96 = 5.66
1.96 + -2.8x + x2 = 5.66

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 5.66

Calculate the square root of the right side: 2.379075451

Break this problem into two subproblems by setting 
(x + -1.4) equal to 2.379075451 and -2.379075451.


Subproblem 1
x + -1.4 = 2.379075451

Simplifying
x + -1.4 = 2.379075451

Reorder the terms:
-1.4 + x = 2.379075451

Solving
-1.4 + x = 2.379075451

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 2.379075451 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 2.379075451 + 1.4
x = 2.379075451 + 1.4

Combine like terms: 2.379075451 + 1.4 = 3.779075451
x = 3.779075451

Simplifying
x = 3.779075451


Subproblem 2
x + -1.4 = -2.379075451

Simplifying
x + -1.4 = -2.379075451

Reorder the terms:
-1.4 + x = -2.379075451

Solving
-1.4 + x = -2.379075451

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -2.379075451 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -2.379075451 + 1.4
x = -2.379075451 + 1.4

Combine like terms: -2.379075451 + 1.4 = -0.979075451
x = -0.979075451

Simplifying
x = -0.979075451


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.779075451, -0.979075451}

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