x^2-7x-84=0

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Solution for x^2-7x-84=0 equation: 


Simplifying
x2 + -7x + -84 = 0

Reorder the terms:
-84 + -7x + x2 = 0

Solving
-84 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -7x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -7x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -7x + x2 = 0 + 84
-7x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-7x + x2 = 84

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 = 84 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 84 + 12.25

Combine like terms: 84 + 12.25 = 96.25
12.25 + -7x + x2 = 96.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + -3.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + -3.5 = 9.810708435

Simplifying
x + -3.5 = 9.810708435

Reorder the terms:
-3.5 + x = 9.810708435

Solving
-3.5 + x = 9.810708435

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 = 9.810708435 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 9.810708435 + 3.5
x = 9.810708435 + 3.5

Combine like terms: 9.810708435 + 3.5 = 13.310708435
x = 13.310708435

Simplifying
x = 13.310708435


Subproblem 2
x + -3.5 = -9.810708435

Simplifying
x + -3.5 = -9.810708435

Reorder the terms:
-3.5 + x = -9.810708435

Solving
-3.5 + x = -9.810708435

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 = -9.810708435 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -9.810708435 + 3.5
x = -9.810708435 + 3.5

Combine like terms: -9.810708435 + 3.5 = -6.310708435
x = -6.310708435

Simplifying
x = -6.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.310708435, -6.310708435}

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