16x+x^2=64

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Solution for 16x+x^2=64 equation:


Simplifying
16x + x2 = 64

Solving
16x + x2 = 64

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 16x + 64 + x2 = 0 + 64

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

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

Combine like terms: 0 + 64 = 64
16x + x2 = 64

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 64 + 64

Reorder the terms:
64 + 16x + x2 = 64 + 64

Combine like terms: 64 + 64 = 128
64 + 16x + x2 = 128

Factor a perfect square on the left side:
(x + 8)(x + 8) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + 8) equal to 11.313708499 and -11.313708499.

Subproblem 1

x + 8 = 11.313708499 Simplifying x + 8 = 11.313708499 Reorder the terms: 8 + x = 11.313708499 Solving 8 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.313708499 + -8 x = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 x = 3.313708499 Simplifying x = 3.313708499

Subproblem 2

x + 8 = -11.313708499 Simplifying x + 8 = -11.313708499 Reorder the terms: 8 + x = -11.313708499 Solving 8 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.313708499 + -8 x = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 x = -19.313708499 Simplifying x = -19.313708499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.313708499, -19.313708499}

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