51x^2-500x+1000=0

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Solution for 51x^2-500x+1000=0 equation:


Simplifying
51x2 + -500x + 1000 = 0

Reorder the terms:
1000 + -500x + 51x2 = 0

Solving
1000 + -500x + 51x2 = 0

Solving for variable 'x'.

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

Divide each side by '51'.
19.60784314 + -9.803921569x + x2 = 0

Move the constant term to the right:

Add '-19.60784314' to each side of the equation.
19.60784314 + -9.803921569x + -19.60784314 + x2 = 0 + -19.60784314

Reorder the terms:
19.60784314 + -19.60784314 + -9.803921569x + x2 = 0 + -19.60784314

Combine like terms: 19.60784314 + -19.60784314 = 0.00000000
0.00000000 + -9.803921569x + x2 = 0 + -19.60784314
-9.803921569x + x2 = 0 + -19.60784314

Combine like terms: 0 + -19.60784314 = -19.60784314
-9.803921569x + x2 = -19.60784314

The x term is -9.803921569x.  Take half its coefficient (-4.901960785).
Square it (24.02921954) and add it to both sides.

Add '24.02921954' to each side of the equation.
-9.803921569x + 24.02921954 + x2 = -19.60784314 + 24.02921954

Reorder the terms:
24.02921954 + -9.803921569x + x2 = -19.60784314 + 24.02921954

Combine like terms: -19.60784314 + 24.02921954 = 4.4213764
24.02921954 + -9.803921569x + x2 = 4.4213764

Factor a perfect square on the left side:
(x + -4.901960785)(x + -4.901960785) = 4.4213764

Calculate the square root of the right side: 2.102706922

Break this problem into two subproblems by setting 
(x + -4.901960785) equal to 2.102706922 and -2.102706922.

Subproblem 1

x + -4.901960785 = 2.102706922 Simplifying x + -4.901960785 = 2.102706922 Reorder the terms: -4.901960785 + x = 2.102706922 Solving -4.901960785 + x = 2.102706922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.901960785' to each side of the equation. -4.901960785 + 4.901960785 + x = 2.102706922 + 4.901960785 Combine like terms: -4.901960785 + 4.901960785 = 0.000000000 0.000000000 + x = 2.102706922 + 4.901960785 x = 2.102706922 + 4.901960785 Combine like terms: 2.102706922 + 4.901960785 = 7.004667707 x = 7.004667707 Simplifying x = 7.004667707

Subproblem 2

x + -4.901960785 = -2.102706922 Simplifying x + -4.901960785 = -2.102706922 Reorder the terms: -4.901960785 + x = -2.102706922 Solving -4.901960785 + x = -2.102706922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.901960785' to each side of the equation. -4.901960785 + 4.901960785 + x = -2.102706922 + 4.901960785 Combine like terms: -4.901960785 + 4.901960785 = 0.000000000 0.000000000 + x = -2.102706922 + 4.901960785 x = -2.102706922 + 4.901960785 Combine like terms: -2.102706922 + 4.901960785 = 2.799253863 x = 2.799253863 Simplifying x = 2.799253863

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.004667707, 2.799253863}

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