x*x+7x-81=0

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Solution for x*x+7x-81=0 equation: 


Simplifying
x * x + 7x + -81 = 0

Multiply x * x
x2 + 7x + -81 = 0

Reorder the terms:
-81 + 7x + x2 = 0

Solving
-81 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 7x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 7x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 7x + x2 = 0 + 81
7x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
7x + x2 = 81

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 81 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 81 + 12.25

Combine like terms: 81 + 12.25 = 93.25
12.25 + 7x + x2 = 93.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 93.25

Calculate the square root of the right side: 9.656603958

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.656603958 and -9.656603958.


Subproblem 1
x + 3.5 = 9.656603958

Simplifying
x + 3.5 = 9.656603958

Reorder the terms:
3.5 + x = 9.656603958

Solving
3.5 + x = 9.656603958

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 9.656603958 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 9.656603958 + -3.5
x = 9.656603958 + -3.5

Combine like terms: 9.656603958 + -3.5 = 6.156603958
x = 6.156603958

Simplifying
x = 6.156603958


Subproblem 2
x + 3.5 = -9.656603958

Simplifying
x + 3.5 = -9.656603958

Reorder the terms:
3.5 + x = -9.656603958

Solving
3.5 + x = -9.656603958

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -9.656603958 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -9.656603958 + -3.5
x = -9.656603958 + -3.5

Combine like terms: -9.656603958 + -3.5 = -13.156603958
x = -13.156603958

Simplifying
x = -13.156603958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.156603958, -13.156603958}

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