x^2+16x-528=0

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Solution for x^2+16x-528=0 equation:


Simplifying
x2 + 16x + -528 = 0

Reorder the terms:
-528 + 16x + x2 = 0

Solving
-528 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '528' to each side of the equation.
-528 + 16x + 528 + x2 = 0 + 528

Reorder the terms:
-528 + 528 + 16x + x2 = 0 + 528

Combine like terms: -528 + 528 = 0
0 + 16x + x2 = 0 + 528
16x + x2 = 0 + 528

Combine like terms: 0 + 528 = 528
16x + x2 = 528

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 = 528 + 64

Reorder the terms:
64 + 16x + x2 = 528 + 64

Combine like terms: 528 + 64 = 592
64 + 16x + x2 = 592

Factor a perfect square on the left side:
(x + 8)(x + 8) = 592

Calculate the square root of the right side: 24.331050121

Break this problem into two subproblems by setting 
(x + 8) equal to 24.331050121 and -24.331050121.

Subproblem 1

x + 8 = 24.331050121 Simplifying x + 8 = 24.331050121 Reorder the terms: 8 + x = 24.331050121 Solving 8 + x = 24.331050121 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 = 24.331050121 + -8 Combine like terms: 8 + -8 = 0 0 + x = 24.331050121 + -8 x = 24.331050121 + -8 Combine like terms: 24.331050121 + -8 = 16.331050121 x = 16.331050121 Simplifying x = 16.331050121

Subproblem 2

x + 8 = -24.331050121 Simplifying x + 8 = -24.331050121 Reorder the terms: 8 + x = -24.331050121 Solving 8 + x = -24.331050121 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 = -24.331050121 + -8 Combine like terms: 8 + -8 = 0 0 + x = -24.331050121 + -8 x = -24.331050121 + -8 Combine like terms: -24.331050121 + -8 = -32.331050121 x = -32.331050121 Simplifying x = -32.331050121

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.331050121, -32.331050121}

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