5x^2-37x+6=0

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Solution for 5x^2-37x+6=0 equation:


Simplifying
5x2 + -37x + 6 = 0

Reorder the terms:
6 + -37x + 5x2 = 0

Solving
6 + -37x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + -7.4x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -7.4x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -7.4x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -7.4x + x2 = 0 + -1.2
-7.4x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-7.4x + x2 = -1.2

The x term is -7.4x.  Take half its coefficient (-3.7).
Square it (13.69) and add it to both sides.

Add '13.69' to each side of the equation.
-7.4x + 13.69 + x2 = -1.2 + 13.69

Reorder the terms:
13.69 + -7.4x + x2 = -1.2 + 13.69

Combine like terms: -1.2 + 13.69 = 12.49
13.69 + -7.4x + x2 = 12.49

Factor a perfect square on the left side:
(x + -3.7)(x + -3.7) = 12.49

Calculate the square root of the right side: 3.534119409

Break this problem into two subproblems by setting 
(x + -3.7) equal to 3.534119409 and -3.534119409.

Subproblem 1

x + -3.7 = 3.534119409 Simplifying x + -3.7 = 3.534119409 Reorder the terms: -3.7 + x = 3.534119409 Solving -3.7 + x = 3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = 3.534119409 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = 3.534119409 + 3.7 x = 3.534119409 + 3.7 Combine like terms: 3.534119409 + 3.7 = 7.234119409 x = 7.234119409 Simplifying x = 7.234119409

Subproblem 2

x + -3.7 = -3.534119409 Simplifying x + -3.7 = -3.534119409 Reorder the terms: -3.7 + x = -3.534119409 Solving -3.7 + x = -3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = -3.534119409 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = -3.534119409 + 3.7 x = -3.534119409 + 3.7 Combine like terms: -3.534119409 + 3.7 = 0.165880591 x = 0.165880591 Simplifying x = 0.165880591

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.234119409, 0.165880591}

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