5x^2-80x-11=29

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Solution for 5x^2-80x-11=29 equation:


Simplifying
5x2 + -80x + -11 = 29

Reorder the terms:
-11 + -80x + 5x2 = 29

Solving
-11 + -80x + 5x2 = 29

Solving for variable 'x'.

Reorder the terms:
-11 + -29 + -80x + 5x2 = 29 + -29

Combine like terms: -11 + -29 = -40
-40 + -80x + 5x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-40 + -80x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + -16x + x2 = 0

Solving
-8 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -16x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -16x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -16x + x2 = 0 + 8
-16x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-16x + x2 = 8

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 = 8 + 64

Reorder the terms:
64 + -16x + x2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + -16x + x2 = 72

Factor a perfect square on the left side:
(x + -8)(x + -8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + -8) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + -8 = 8.485281374

Simplifying
x + -8 = 8.485281374

Reorder the terms:
-8 + x = 8.485281374

Solving
-8 + x = 8.485281374

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 = 8.485281374 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.485281374 + 8
x = 8.485281374 + 8

Combine like terms: 8.485281374 + 8 = 16.485281374
x = 16.485281374

Simplifying
x = 16.485281374


Subproblem 2
x + -8 = -8.485281374

Simplifying
x + -8 = -8.485281374

Reorder the terms:
-8 + x = -8.485281374

Solving
-8 + x = -8.485281374

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 = -8.485281374 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.485281374 + 8
x = -8.485281374 + 8

Combine like terms: -8.485281374 + 8 = -0.485281374
x = -0.485281374

Simplifying
x = -0.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.485281374, -0.485281374}
Solution
x = {16.485281374, -0.485281374}

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