x^2-3.7x+2=0

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


Simplifying
x2 + -3.7x + 2 = 0

Reorder the terms:
2 + -3.7x + x2 = 0

Solving
2 + -3.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.7x + x2 = 0 + -2
-3.7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.7x + x2 = -2

The x term is -3.7x.  Take half its coefficient (-1.85).
Square it (3.4225) and add it to both sides.

Add '3.4225' to each side of the equation.
-3.7x + 3.4225 + x2 = -2 + 3.4225

Reorder the terms:
3.4225 + -3.7x + x2 = -2 + 3.4225

Combine like terms: -2 + 3.4225 = 1.4225
3.4225 + -3.7x + x2 = 1.4225

Factor a perfect square on the left side:
(x + -1.85)(x + -1.85) = 1.4225

Calculate the square root of the right side: 1.192686044

Break this problem into two subproblems by setting 
(x + -1.85) equal to 1.192686044 and -1.192686044.

Subproblem 1

x + -1.85 = 1.192686044 Simplifying x + -1.85 = 1.192686044 Reorder the terms: -1.85 + x = 1.192686044 Solving -1.85 + x = 1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = 1.192686044 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = 1.192686044 + 1.85 x = 1.192686044 + 1.85 Combine like terms: 1.192686044 + 1.85 = 3.042686044 x = 3.042686044 Simplifying x = 3.042686044

Subproblem 2

x + -1.85 = -1.192686044 Simplifying x + -1.85 = -1.192686044 Reorder the terms: -1.85 + x = -1.192686044 Solving -1.85 + x = -1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = -1.192686044 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = -1.192686044 + 1.85 x = -1.192686044 + 1.85 Combine like terms: -1.192686044 + 1.85 = 0.657313956 x = 0.657313956 Simplifying x = 0.657313956

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.042686044, 0.657313956}

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