9x^2+18x-77=7

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Solution for 9x^2+18x-77=7 equation: 


Simplifying
9x2 + 18x + -77 = 7

Reorder the terms:
-77 + 18x + 9x2 = 7

Solving
-77 + 18x + 9x2 = 7

Solving for variable 'x'.

Reorder the terms:
-77 + -7 + 18x + 9x2 = 7 + -7

Combine like terms: -77 + -7 = -84
-84 + 18x + 9x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-84 + 18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + 6x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-28 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-28 + 6x + 3x2 = 0

Solving
-28 + 6x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-9.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 2x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 2x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 9.333333333
2x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
2x + x2 = 9.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 9.333333333 + 1

Combine like terms: 9.333333333 + 1 = 10.333333333
1 + 2x + x2 = 10.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10.333333333

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(x + 1) equal to 3.214550254 and -3.214550254.


Subproblem 1
x + 1 = 3.214550254

Simplifying
x + 1 = 3.214550254

Reorder the terms:
1 + x = 3.214550254

Solving
1 + x = 3.214550254

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.214550254 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.214550254 + -1
x = 3.214550254 + -1

Combine like terms: 3.214550254 + -1 = 2.214550254
x = 2.214550254

Simplifying
x = 2.214550254


Subproblem 2
x + 1 = -3.214550254

Simplifying
x + 1 = -3.214550254

Reorder the terms:
1 + x = -3.214550254

Solving
1 + x = -3.214550254

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.214550254 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.214550254 + -1
x = -3.214550254 + -1

Combine like terms: -3.214550254 + -1 = -4.214550254
x = -4.214550254

Simplifying
x = -4.214550254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.214550254, -4.214550254}
Solution
x = {2.214550254, -4.214550254}

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