49x^2-600x+80=

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Solution for 49x^2-600x+80= equation:


Simplifying
49x2 + -600x + 80 = 0

Reorder the terms:
80 + -600x + 49x2 = 0

Solving
80 + -600x + 49x2 = 0

Solving for variable 'x'.

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

Divide each side by '49'.
1.632653061 + -12.24489796x + x2 = 0

Move the constant term to the right:

Add '-1.632653061' to each side of the equation.
1.632653061 + -12.24489796x + -1.632653061 + x2 = 0 + -1.632653061

Reorder the terms:
1.632653061 + -1.632653061 + -12.24489796x + x2 = 0 + -1.632653061

Combine like terms: 1.632653061 + -1.632653061 = 0.000000000
0.000000000 + -12.24489796x + x2 = 0 + -1.632653061
-12.24489796x + x2 = 0 + -1.632653061

Combine like terms: 0 + -1.632653061 = -1.632653061
-12.24489796x + x2 = -1.632653061

The x term is -12.24489796x.  Take half its coefficient (-6.12244898).
Square it (37.48438151) and add it to both sides.

Add '37.48438151' to each side of the equation.
-12.24489796x + 37.48438151 + x2 = -1.632653061 + 37.48438151

Reorder the terms:
37.48438151 + -12.24489796x + x2 = -1.632653061 + 37.48438151

Combine like terms: -1.632653061 + 37.48438151 = 35.851728449
37.48438151 + -12.24489796x + x2 = 35.851728449

Factor a perfect square on the left side:
(x + -6.12244898)(x + -6.12244898) = 35.851728449

Calculate the square root of the right side: 5.987631289

Break this problem into two subproblems by setting 
(x + -6.12244898) equal to 5.987631289 and -5.987631289.

Subproblem 1

x + -6.12244898 = 5.987631289 Simplifying x + -6.12244898 = 5.987631289 Reorder the terms: -6.12244898 + x = 5.987631289 Solving -6.12244898 + x = 5.987631289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + x = 5.987631289 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + x = 5.987631289 + 6.12244898 x = 5.987631289 + 6.12244898 Combine like terms: 5.987631289 + 6.12244898 = 12.110080269 x = 12.110080269 Simplifying x = 12.110080269

Subproblem 2

x + -6.12244898 = -5.987631289 Simplifying x + -6.12244898 = -5.987631289 Reorder the terms: -6.12244898 + x = -5.987631289 Solving -6.12244898 + x = -5.987631289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + x = -5.987631289 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + x = -5.987631289 + 6.12244898 x = -5.987631289 + 6.12244898 Combine like terms: -5.987631289 + 6.12244898 = 0.134817691 x = 0.134817691 Simplifying x = 0.134817691

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.110080269, 0.134817691}

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