2x^2+100x-658469=0

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Solution for 2x^2+100x-658469=0 equation:


Simplifying
2x2 + 100x + -658469 = 0

Reorder the terms:
-658469 + 100x + 2x2 = 0

Solving
-658469 + 100x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-329234.5 + 50x + x2 = 0

Move the constant term to the right:

Add '329234.5' to each side of the equation.
-329234.5 + 50x + 329234.5 + x2 = 0 + 329234.5

Reorder the terms:
-329234.5 + 329234.5 + 50x + x2 = 0 + 329234.5

Combine like terms: -329234.5 + 329234.5 = 0.0
0.0 + 50x + x2 = 0 + 329234.5
50x + x2 = 0 + 329234.5

Combine like terms: 0 + 329234.5 = 329234.5
50x + x2 = 329234.5

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 329234.5 + 625

Reorder the terms:
625 + 50x + x2 = 329234.5 + 625

Combine like terms: 329234.5 + 625 = 329859.5
625 + 50x + x2 = 329859.5

Factor a perfect square on the left side:
(x + 25)(x + 25) = 329859.5

Calculate the square root of the right side: 574.333962081

Break this problem into two subproblems by setting 
(x + 25) equal to 574.333962081 and -574.333962081.

Subproblem 1

x + 25 = 574.333962081 Simplifying x + 25 = 574.333962081 Reorder the terms: 25 + x = 574.333962081 Solving 25 + x = 574.333962081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 574.333962081 + -25 Combine like terms: 25 + -25 = 0 0 + x = 574.333962081 + -25 x = 574.333962081 + -25 Combine like terms: 574.333962081 + -25 = 549.333962081 x = 549.333962081 Simplifying x = 549.333962081

Subproblem 2

x + 25 = -574.333962081 Simplifying x + 25 = -574.333962081 Reorder the terms: 25 + x = -574.333962081 Solving 25 + x = -574.333962081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -574.333962081 + -25 Combine like terms: 25 + -25 = 0 0 + x = -574.333962081 + -25 x = -574.333962081 + -25 Combine like terms: -574.333962081 + -25 = -599.333962081 x = -599.333962081 Simplifying x = -599.333962081

Solution

The solution to the problem is based on the solutions from the subproblems. x = {549.333962081, -599.333962081}

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