11.4x^2-183.4x+300=0

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Solution for 11.4x^2-183.4x+300=0 equation:


Simplifying
11.4x2 + -183.4x + 300 = 0

Reorder the terms:
300 + -183.4x + 11.4x2 = 0

Solving
300 + -183.4x + 11.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '11.4'.
26.31578947 + -16.0877193x + x2 = 0

Move the constant term to the right:

Add '-26.31578947' to each side of the equation.
26.31578947 + -16.0877193x + -26.31578947 + x2 = 0 + -26.31578947

Reorder the terms:
26.31578947 + -26.31578947 + -16.0877193x + x2 = 0 + -26.31578947

Combine like terms: 26.31578947 + -26.31578947 = 0.00000000
0.00000000 + -16.0877193x + x2 = 0 + -26.31578947
-16.0877193x + x2 = 0 + -26.31578947

Combine like terms: 0 + -26.31578947 = -26.31578947
-16.0877193x + x2 = -26.31578947

The x term is -16.0877193x.  Take half its coefficient (-8.04385965).
Square it (64.70367807) and add it to both sides.

Add '64.70367807' to each side of the equation.
-16.0877193x + 64.70367807 + x2 = -26.31578947 + 64.70367807

Reorder the terms:
64.70367807 + -16.0877193x + x2 = -26.31578947 + 64.70367807

Combine like terms: -26.31578947 + 64.70367807 = 38.3878886
64.70367807 + -16.0877193x + x2 = 38.3878886

Factor a perfect square on the left side:
(x + -8.04385965)(x + -8.04385965) = 38.3878886

Calculate the square root of the right side: 6.195796042

Break this problem into two subproblems by setting 
(x + -8.04385965) equal to 6.195796042 and -6.195796042.

Subproblem 1

x + -8.04385965 = 6.195796042 Simplifying x + -8.04385965 = 6.195796042 Reorder the terms: -8.04385965 + x = 6.195796042 Solving -8.04385965 + x = 6.195796042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.04385965' to each side of the equation. -8.04385965 + 8.04385965 + x = 6.195796042 + 8.04385965 Combine like terms: -8.04385965 + 8.04385965 = 0.00000000 0.00000000 + x = 6.195796042 + 8.04385965 x = 6.195796042 + 8.04385965 Combine like terms: 6.195796042 + 8.04385965 = 14.239655692 x = 14.239655692 Simplifying x = 14.239655692

Subproblem 2

x + -8.04385965 = -6.195796042 Simplifying x + -8.04385965 = -6.195796042 Reorder the terms: -8.04385965 + x = -6.195796042 Solving -8.04385965 + x = -6.195796042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.04385965' to each side of the equation. -8.04385965 + 8.04385965 + x = -6.195796042 + 8.04385965 Combine like terms: -8.04385965 + 8.04385965 = 0.00000000 0.00000000 + x = -6.195796042 + 8.04385965 x = -6.195796042 + 8.04385965 Combine like terms: -6.195796042 + 8.04385965 = 1.848063608 x = 1.848063608 Simplifying x = 1.848063608

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.239655692, 1.848063608}

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