(x*x)+160x=6000

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Solution for (x*x)+160x=6000 equation:


Simplifying
(x * x) + 160x = 6000

Multiply x * x
(x2) + 160x = 6000
x2 + 160x = 6000

Reorder the terms:
160x + x2 = 6000

Solving
160x + x2 = 6000

Solving for variable 'x'.

Reorder the terms:
-6000 + 160x + x2 = 6000 + -6000

Combine like terms: 6000 + -6000 = 0
-6000 + 160x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6000' to each side of the equation.
-6000 + 160x + 6000 + x2 = 0 + 6000

Reorder the terms:
-6000 + 6000 + 160x + x2 = 0 + 6000

Combine like terms: -6000 + 6000 = 0
0 + 160x + x2 = 0 + 6000
160x + x2 = 0 + 6000

Combine like terms: 0 + 6000 = 6000
160x + x2 = 6000

The x term is 160x.  Take half its coefficient (80).
Square it (6400) and add it to both sides.

Add '6400' to each side of the equation.
160x + 6400 + x2 = 6000 + 6400

Reorder the terms:
6400 + 160x + x2 = 6000 + 6400

Combine like terms: 6000 + 6400 = 12400
6400 + 160x + x2 = 12400

Factor a perfect square on the left side:
(x + 80)(x + 80) = 12400

Calculate the square root of the right side: 111.355287257

Break this problem into two subproblems by setting 
(x + 80) equal to 111.355287257 and -111.355287257.

Subproblem 1

x + 80 = 111.355287257 Simplifying x + 80 = 111.355287257 Reorder the terms: 80 + x = 111.355287257 Solving 80 + x = 111.355287257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 111.355287257 + -80 Combine like terms: 80 + -80 = 0 0 + x = 111.355287257 + -80 x = 111.355287257 + -80 Combine like terms: 111.355287257 + -80 = 31.355287257 x = 31.355287257 Simplifying x = 31.355287257

Subproblem 2

x + 80 = -111.355287257 Simplifying x + 80 = -111.355287257 Reorder the terms: 80 + x = -111.355287257 Solving 80 + x = -111.355287257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -111.355287257 + -80 Combine like terms: 80 + -80 = 0 0 + x = -111.355287257 + -80 x = -111.355287257 + -80 Combine like terms: -111.355287257 + -80 = -191.355287257 x = -191.355287257 Simplifying x = -191.355287257

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.355287257, -191.355287257}

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