x^2+300x=15000

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Solution for x^2+300x=15000 equation:


Simplifying
x2 + 300x = 15000

Reorder the terms:
300x + x2 = 15000

Solving
300x + x2 = 15000

Solving for variable 'x'.

Reorder the terms:
-15000 + 300x + x2 = 15000 + -15000

Combine like terms: 15000 + -15000 = 0
-15000 + 300x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15000' to each side of the equation.
-15000 + 300x + 15000 + x2 = 0 + 15000

Reorder the terms:
-15000 + 15000 + 300x + x2 = 0 + 15000

Combine like terms: -15000 + 15000 = 0
0 + 300x + x2 = 0 + 15000
300x + x2 = 0 + 15000

Combine like terms: 0 + 15000 = 15000
300x + x2 = 15000

The x term is 300x.  Take half its coefficient (150).
Square it (22500) and add it to both sides.

Add '22500' to each side of the equation.
300x + 22500 + x2 = 15000 + 22500

Reorder the terms:
22500 + 300x + x2 = 15000 + 22500

Combine like terms: 15000 + 22500 = 37500
22500 + 300x + x2 = 37500

Factor a perfect square on the left side:
(x + 150)(x + 150) = 37500

Calculate the square root of the right side: 193.64916731

Break this problem into two subproblems by setting 
(x + 150) equal to 193.64916731 and -193.64916731.

Subproblem 1

x + 150 = 193.64916731 Simplifying x + 150 = 193.64916731 Reorder the terms: 150 + x = 193.64916731 Solving 150 + x = 193.64916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 193.64916731 + -150 Combine like terms: 150 + -150 = 0 0 + x = 193.64916731 + -150 x = 193.64916731 + -150 Combine like terms: 193.64916731 + -150 = 43.64916731 x = 43.64916731 Simplifying x = 43.64916731

Subproblem 2

x + 150 = -193.64916731 Simplifying x + 150 = -193.64916731 Reorder the terms: 150 + x = -193.64916731 Solving 150 + x = -193.64916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -193.64916731 + -150 Combine like terms: 150 + -150 = 0 0 + x = -193.64916731 + -150 x = -193.64916731 + -150 Combine like terms: -193.64916731 + -150 = -343.64916731 x = -343.64916731 Simplifying x = -343.64916731

Solution

The solution to the problem is based on the solutions from the subproblems. x = {43.64916731, -343.64916731}

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