x^2+250x-625000=0

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Solution for x^2+250x-625000=0 equation:


Simplifying
x2 + 250x + -625000 = 0

Reorder the terms:
-625000 + 250x + x2 = 0

Solving
-625000 + 250x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '625000' to each side of the equation.
-625000 + 250x + 625000 + x2 = 0 + 625000

Reorder the terms:
-625000 + 625000 + 250x + x2 = 0 + 625000

Combine like terms: -625000 + 625000 = 0
0 + 250x + x2 = 0 + 625000
250x + x2 = 0 + 625000

Combine like terms: 0 + 625000 = 625000
250x + x2 = 625000

The x term is 250x.  Take half its coefficient (125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
250x + 15625 + x2 = 625000 + 15625

Reorder the terms:
15625 + 250x + x2 = 625000 + 15625

Combine like terms: 625000 + 15625 = 640625
15625 + 250x + x2 = 640625

Factor a perfect square on the left side:
(x + 125)(x + 125) = 640625

Calculate the square root of the right side: 800.390529679

Break this problem into two subproblems by setting 
(x + 125) equal to 800.390529679 and -800.390529679.

Subproblem 1

x + 125 = 800.390529679 Simplifying x + 125 = 800.390529679 Reorder the terms: 125 + x = 800.390529679 Solving 125 + x = 800.390529679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = 800.390529679 + -125 Combine like terms: 125 + -125 = 0 0 + x = 800.390529679 + -125 x = 800.390529679 + -125 Combine like terms: 800.390529679 + -125 = 675.390529679 x = 675.390529679 Simplifying x = 675.390529679

Subproblem 2

x + 125 = -800.390529679 Simplifying x + 125 = -800.390529679 Reorder the terms: 125 + x = -800.390529679 Solving 125 + x = -800.390529679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = -800.390529679 + -125 Combine like terms: 125 + -125 = 0 0 + x = -800.390529679 + -125 x = -800.390529679 + -125 Combine like terms: -800.390529679 + -125 = -925.390529679 x = -925.390529679 Simplifying x = -925.390529679

Solution

The solution to the problem is based on the solutions from the subproblems. x = {675.390529679, -925.390529679}

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