x^2+600x-60=0

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Solution for x^2+600x-60=0 equation:


Simplifying
x2 + 600x + -60 = 0

Reorder the terms:
-60 + 600x + x2 = 0

Solving
-60 + 600x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 600x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 600x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 600x + x2 = 0 + 60
600x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
600x + x2 = 60

The x term is 600x.  Take half its coefficient (300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
600x + 90000 + x2 = 60 + 90000

Reorder the terms:
90000 + 600x + x2 = 60 + 90000

Combine like terms: 60 + 90000 = 90060
90000 + 600x + x2 = 90060

Factor a perfect square on the left side:
(x + 300)(x + 300) = 90060

Calculate the square root of the right side: 300.099983339

Break this problem into two subproblems by setting 
(x + 300) equal to 300.099983339 and -300.099983339.

Subproblem 1

x + 300 = 300.099983339 Simplifying x + 300 = 300.099983339 Reorder the terms: 300 + x = 300.099983339 Solving 300 + x = 300.099983339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 300.099983339 + -300 Combine like terms: 300 + -300 = 0 0 + x = 300.099983339 + -300 x = 300.099983339 + -300 Combine like terms: 300.099983339 + -300 = 0.099983339 x = 0.099983339 Simplifying x = 0.099983339

Subproblem 2

x + 300 = -300.099983339 Simplifying x + 300 = -300.099983339 Reorder the terms: 300 + x = -300.099983339 Solving 300 + x = -300.099983339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -300.099983339 + -300 Combine like terms: 300 + -300 = 0 0 + x = -300.099983339 + -300 x = -300.099983339 + -300 Combine like terms: -300.099983339 + -300 = -600.099983339 x = -600.099983339 Simplifying x = -600.099983339

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.099983339, -600.099983339}

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