5x^2-50x+c=12+c

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Solution for 5x^2-50x+c=12+c equation:


Simplifying
5x2 + -50x + c = 12 + c

Reorder the terms:
c + -50x + 5x2 = 12 + c

Add '-1c' to each side of the equation.
c + -50x + -1c + 5x2 = 12 + c + -1c

Reorder the terms:
c + -1c + -50x + 5x2 = 12 + c + -1c

Combine like terms: c + -1c = 0
0 + -50x + 5x2 = 12 + c + -1c
-50x + 5x2 = 12 + c + -1c

Combine like terms: c + -1c = 0
-50x + 5x2 = 12 + 0
-50x + 5x2 = 12

Solving
-50x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -50x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -50x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + -10x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -10x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -10x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -10x + x2 = 0 + 2.4
-10x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-10x + x2 = 2.4

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 2.4 + 25

Reorder the terms:
25 + -10x + x2 = 2.4 + 25

Combine like terms: 2.4 + 25 = 27.4
25 + -10x + x2 = 27.4

Factor a perfect square on the left side:
(x + -5)(x + -5) = 27.4

Calculate the square root of the right side: 5.234500931

Break this problem into two subproblems by setting 
(x + -5) equal to 5.234500931 and -5.234500931.

Subproblem 1

x + -5 = 5.234500931 Simplifying x + -5 = 5.234500931 Reorder the terms: -5 + x = 5.234500931 Solving -5 + x = 5.234500931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.234500931 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.234500931 + 5 x = 5.234500931 + 5 Combine like terms: 5.234500931 + 5 = 10.234500931 x = 10.234500931 Simplifying x = 10.234500931

Subproblem 2

x + -5 = -5.234500931 Simplifying x + -5 = -5.234500931 Reorder the terms: -5 + x = -5.234500931 Solving -5 + x = -5.234500931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.234500931 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.234500931 + 5 x = -5.234500931 + 5 Combine like terms: -5.234500931 + 5 = -0.234500931 x = -0.234500931 Simplifying x = -0.234500931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.234500931, -0.234500931}

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