x^2+128x=220

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Solution for x^2+128x=220 equation:


Simplifying
x2 + 128x = 220

Reorder the terms:
128x + x2 = 220

Solving
128x + x2 = 220

Solving for variable 'x'.

Reorder the terms:
-220 + 128x + x2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + 128x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '220' to each side of the equation.
-220 + 128x + 220 + x2 = 0 + 220

Reorder the terms:
-220 + 220 + 128x + x2 = 0 + 220

Combine like terms: -220 + 220 = 0
0 + 128x + x2 = 0 + 220
128x + x2 = 0 + 220

Combine like terms: 0 + 220 = 220
128x + x2 = 220

The x term is 128x.  Take half its coefficient (64).
Square it (4096) and add it to both sides.

Add '4096' to each side of the equation.
128x + 4096 + x2 = 220 + 4096

Reorder the terms:
4096 + 128x + x2 = 220 + 4096

Combine like terms: 220 + 4096 = 4316
4096 + 128x + x2 = 4316

Factor a perfect square on the left side:
(x + 64)(x + 64) = 4316

Calculate the square root of the right side: 65.696270823

Break this problem into two subproblems by setting 
(x + 64) equal to 65.696270823 and -65.696270823.

Subproblem 1

x + 64 = 65.696270823 Simplifying x + 64 = 65.696270823 Reorder the terms: 64 + x = 65.696270823 Solving 64 + x = 65.696270823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = 65.696270823 + -64 Combine like terms: 64 + -64 = 0 0 + x = 65.696270823 + -64 x = 65.696270823 + -64 Combine like terms: 65.696270823 + -64 = 1.696270823 x = 1.696270823 Simplifying x = 1.696270823

Subproblem 2

x + 64 = -65.696270823 Simplifying x + 64 = -65.696270823 Reorder the terms: 64 + x = -65.696270823 Solving 64 + x = -65.696270823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = -65.696270823 + -64 Combine like terms: 64 + -64 = 0 0 + x = -65.696270823 + -64 x = -65.696270823 + -64 Combine like terms: -65.696270823 + -64 = -129.696270823 x = -129.696270823 Simplifying x = -129.696270823

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.696270823, -129.696270823}

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