50x^2-2.5x-4975=0

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Solution for 50x^2-2.5x-4975=0 equation:


Simplifying
50x2 + -2.5x + -4975 = 0

Reorder the terms:
-4975 + -2.5x + 50x2 = 0

Solving
-4975 + -2.5x + 50x2 = 0

Solving for variable 'x'.

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

Divide each side by '50'.
-99.5 + -0.05x + x2 = 0

Move the constant term to the right:

Add '99.5' to each side of the equation.
-99.5 + -0.05x + 99.5 + x2 = 0 + 99.5

Reorder the terms:
-99.5 + 99.5 + -0.05x + x2 = 0 + 99.5

Combine like terms: -99.5 + 99.5 = 0.0
0.0 + -0.05x + x2 = 0 + 99.5
-0.05x + x2 = 0 + 99.5

Combine like terms: 0 + 99.5 = 99.5
-0.05x + x2 = 99.5

The x term is -0.05x.  Take half its coefficient (-0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
-0.05x + 0.000625 + x2 = 99.5 + 0.000625

Reorder the terms:
0.000625 + -0.05x + x2 = 99.5 + 0.000625

Combine like terms: 99.5 + 0.000625 = 99.500625
0.000625 + -0.05x + x2 = 99.500625

Factor a perfect square on the left side:
(x + -0.025)(x + -0.025) = 99.500625

Calculate the square root of the right side: 9.975

Break this problem into two subproblems by setting 
(x + -0.025) equal to 9.975 and -9.975.

Subproblem 1

x + -0.025 = 9.975 Simplifying x + -0.025 = 9.975 Reorder the terms: -0.025 + x = 9.975 Solving -0.025 + x = 9.975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 9.975 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 9.975 + 0.025 x = 9.975 + 0.025 Combine like terms: 9.975 + 0.025 = 10 x = 10 Simplifying x = 10

Subproblem 2

x + -0.025 = -9.975 Simplifying x + -0.025 = -9.975 Reorder the terms: -0.025 + x = -9.975 Solving -0.025 + x = -9.975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -9.975 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -9.975 + 0.025 x = -9.975 + 0.025 Combine like terms: -9.975 + 0.025 = -9.95 x = -9.95 Simplifying x = -9.95

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10, -9.95}

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