x^2+1600x=2320

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Solution for x^2+1600x=2320 equation:


Simplifying
x2 + 1600x = 2320

Reorder the terms:
1600x + x2 = 2320

Solving
1600x + x2 = 2320

Solving for variable 'x'.

Reorder the terms:
-2320 + 1600x + x2 = 2320 + -2320

Combine like terms: 2320 + -2320 = 0
-2320 + 1600x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2320' to each side of the equation.
-2320 + 1600x + 2320 + x2 = 0 + 2320

Reorder the terms:
-2320 + 2320 + 1600x + x2 = 0 + 2320

Combine like terms: -2320 + 2320 = 0
0 + 1600x + x2 = 0 + 2320
1600x + x2 = 0 + 2320

Combine like terms: 0 + 2320 = 2320
1600x + x2 = 2320

The x term is 1600x.  Take half its coefficient (800).
Square it (640000) and add it to both sides.

Add '640000' to each side of the equation.
1600x + 640000 + x2 = 2320 + 640000

Reorder the terms:
640000 + 1600x + x2 = 2320 + 640000

Combine like terms: 2320 + 640000 = 642320
640000 + 1600x + x2 = 642320

Factor a perfect square on the left side:
(x + 800)(x + 800) = 642320

Calculate the square root of the right side: 801.448688314

Break this problem into two subproblems by setting 
(x + 800) equal to 801.448688314 and -801.448688314.

Subproblem 1

x + 800 = 801.448688314 Simplifying x + 800 = 801.448688314 Reorder the terms: 800 + x = 801.448688314 Solving 800 + x = 801.448688314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-800' to each side of the equation. 800 + -800 + x = 801.448688314 + -800 Combine like terms: 800 + -800 = 0 0 + x = 801.448688314 + -800 x = 801.448688314 + -800 Combine like terms: 801.448688314 + -800 = 1.448688314 x = 1.448688314 Simplifying x = 1.448688314

Subproblem 2

x + 800 = -801.448688314 Simplifying x + 800 = -801.448688314 Reorder the terms: 800 + x = -801.448688314 Solving 800 + x = -801.448688314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-800' to each side of the equation. 800 + -800 + x = -801.448688314 + -800 Combine like terms: 800 + -800 = 0 0 + x = -801.448688314 + -800 x = -801.448688314 + -800 Combine like terms: -801.448688314 + -800 = -1601.448688314 x = -1601.448688314 Simplifying x = -1601.448688314

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.448688314, -1601.448688314}

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