x^2+16x+64-100x=0

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Solution for x^2+16x+64-100x=0 equation:


Simplifying
x2 + 16x + 64 + -100x = 0

Reorder the terms:
64 + 16x + -100x + x2 = 0

Combine like terms: 16x + -100x = -84x
64 + -84x + x2 = 0

Solving
64 + -84x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -84x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -84x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -84x + x2 = 0 + -64
-84x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-84x + x2 = -64

The x term is -84x.  Take half its coefficient (-42).
Square it (1764) and add it to both sides.

Add '1764' to each side of the equation.
-84x + 1764 + x2 = -64 + 1764

Reorder the terms:
1764 + -84x + x2 = -64 + 1764

Combine like terms: -64 + 1764 = 1700
1764 + -84x + x2 = 1700

Factor a perfect square on the left side:
(x + -42)(x + -42) = 1700

Calculate the square root of the right side: 41.231056256

Break this problem into two subproblems by setting 
(x + -42) equal to 41.231056256 and -41.231056256.

Subproblem 1

x + -42 = 41.231056256 Simplifying x + -42 = 41.231056256 Reorder the terms: -42 + x = 41.231056256 Solving -42 + x = 41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = 41.231056256 + 42 Combine like terms: -42 + 42 = 0 0 + x = 41.231056256 + 42 x = 41.231056256 + 42 Combine like terms: 41.231056256 + 42 = 83.231056256 x = 83.231056256 Simplifying x = 83.231056256

Subproblem 2

x + -42 = -41.231056256 Simplifying x + -42 = -41.231056256 Reorder the terms: -42 + x = -41.231056256 Solving -42 + x = -41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = -41.231056256 + 42 Combine like terms: -42 + 42 = 0 0 + x = -41.231056256 + 42 x = -41.231056256 + 42 Combine like terms: -41.231056256 + 42 = 0.768943744 x = 0.768943744 Simplifying x = 0.768943744

Solution

The solution to the problem is based on the solutions from the subproblems. x = {83.231056256, 0.768943744}

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