x^2+9x-16=0

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Solution for x^2+9x-16=0 equation: 


Simplifying
x2 + 9x + -16 = 0

Reorder the terms:
-16 + 9x + x2 = 0

Solving
-16 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 9x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 9x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 9x + x2 = 0 + 16
9x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
9x + x2 = 16

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 16 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + 9x + x2 = 36.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + 4.5 = 6.020797289

Simplifying
x + 4.5 = 6.020797289

Reorder the terms:
4.5 + x = 6.020797289

Solving
4.5 + x = 6.020797289

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.020797289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.020797289 + -4.5
x = 6.020797289 + -4.5

Combine like terms: 6.020797289 + -4.5 = 1.520797289
x = 1.520797289

Simplifying
x = 1.520797289


Subproblem 2
x + 4.5 = -6.020797289

Simplifying
x + 4.5 = -6.020797289

Reorder the terms:
4.5 + x = -6.020797289

Solving
4.5 + x = -6.020797289

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.020797289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.020797289 + -4.5
x = -6.020797289 + -4.5

Combine like terms: -6.020797289 + -4.5 = -10.520797289
x = -10.520797289

Simplifying
x = -10.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.520797289, -10.520797289}

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