2x^2+9x-48600=0

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Solution for 2x^2+9x-48600=0 equation:


Simplifying
2x2 + 9x + -48600 = 0

Reorder the terms:
-48600 + 9x + 2x2 = 0

Solving
-48600 + 9x + 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'.
-24300 + 4.5x + x2 = 0

Move the constant term to the right:

Add '24300' to each side of the equation.
-24300 + 4.5x + 24300 + x2 = 0 + 24300

Reorder the terms:
-24300 + 24300 + 4.5x + x2 = 0 + 24300

Combine like terms: -24300 + 24300 = 0
0 + 4.5x + x2 = 0 + 24300
4.5x + x2 = 0 + 24300

Combine like terms: 0 + 24300 = 24300
4.5x + x2 = 24300

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 24300 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 24300 + 5.0625

Combine like terms: 24300 + 5.0625 = 24305.0625
5.0625 + 4.5x + x2 = 24305.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 24305.0625

Calculate the square root of the right side: 155.900809812

Break this problem into two subproblems by setting 
(x + 2.25) equal to 155.900809812 and -155.900809812.

Subproblem 1

x + 2.25 = 155.900809812 Simplifying x + 2.25 = 155.900809812 Reorder the terms: 2.25 + x = 155.900809812 Solving 2.25 + x = 155.900809812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 155.900809812 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 155.900809812 + -2.25 x = 155.900809812 + -2.25 Combine like terms: 155.900809812 + -2.25 = 153.650809812 x = 153.650809812 Simplifying x = 153.650809812

Subproblem 2

x + 2.25 = -155.900809812 Simplifying x + 2.25 = -155.900809812 Reorder the terms: 2.25 + x = -155.900809812 Solving 2.25 + x = -155.900809812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -155.900809812 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -155.900809812 + -2.25 x = -155.900809812 + -2.25 Combine like terms: -155.900809812 + -2.25 = -158.150809812 x = -158.150809812 Simplifying x = -158.150809812

Solution

The solution to the problem is based on the solutions from the subproblems. x = {153.650809812, -158.150809812}

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