2x^2-45x+37.4=0

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Solution for 2x^2-45x+37.4=0 equation:


Simplifying
2x2 + -45x + 37.4 = 0

Reorder the terms:
37.4 + -45x + 2x2 = 0

Solving
37.4 + -45x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
18.7 + -22.5x + x2 = 0

Move the constant term to the right:

Add '-18.7' to each side of the equation.
18.7 + -22.5x + -18.7 + x2 = 0 + -18.7

Reorder the terms:
18.7 + -18.7 + -22.5x + x2 = 0 + -18.7

Combine like terms: 18.7 + -18.7 = 0.0
0.0 + -22.5x + x2 = 0 + -18.7
-22.5x + x2 = 0 + -18.7

Combine like terms: 0 + -18.7 = -18.7
-22.5x + x2 = -18.7

The x term is -22.5x.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5x + 126.5625 + x2 = -18.7 + 126.5625

Reorder the terms:
126.5625 + -22.5x + x2 = -18.7 + 126.5625

Combine like terms: -18.7 + 126.5625 = 107.8625
126.5625 + -22.5x + x2 = 107.8625

Factor a perfect square on the left side:
(x + -11.25)(x + -11.25) = 107.8625

Calculate the square root of the right side: 10.385687267

Break this problem into two subproblems by setting 
(x + -11.25) equal to 10.385687267 and -10.385687267.

Subproblem 1

x + -11.25 = 10.385687267 Simplifying x + -11.25 = 10.385687267 Reorder the terms: -11.25 + x = 10.385687267 Solving -11.25 + x = 10.385687267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 10.385687267 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 10.385687267 + 11.25 x = 10.385687267 + 11.25 Combine like terms: 10.385687267 + 11.25 = 21.635687267 x = 21.635687267 Simplifying x = 21.635687267

Subproblem 2

x + -11.25 = -10.385687267 Simplifying x + -11.25 = -10.385687267 Reorder the terms: -11.25 + x = -10.385687267 Solving -11.25 + x = -10.385687267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -10.385687267 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -10.385687267 + 11.25 x = -10.385687267 + 11.25 Combine like terms: -10.385687267 + 11.25 = 0.864312733 x = 0.864312733 Simplifying x = 0.864312733

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.635687267, 0.864312733}

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