7x(11x+9)=135

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Solution for 7x(11x+9)=135 equation:


Simplifying
7x(11x + 9) = 135

Reorder the terms:
7x(9 + 11x) = 135
(9 * 7x + 11x * 7x) = 135
(63x + 77x2) = 135

Solving
63x + 77x2 = 135

Solving for variable 'x'.

Reorder the terms:
-135 + 63x + 77x2 = 135 + -135

Combine like terms: 135 + -135 = 0
-135 + 63x + 77x2 = 0

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

Divide each side by '77'.
-1.753246753 + 0.8181818182x + x2 = 0

Move the constant term to the right:

Add '1.753246753' to each side of the equation.
-1.753246753 + 0.8181818182x + 1.753246753 + x2 = 0 + 1.753246753

Reorder the terms:
-1.753246753 + 1.753246753 + 0.8181818182x + x2 = 0 + 1.753246753

Combine like terms: -1.753246753 + 1.753246753 = 0.000000000
0.000000000 + 0.8181818182x + x2 = 0 + 1.753246753
0.8181818182x + x2 = 0 + 1.753246753

Combine like terms: 0 + 1.753246753 = 1.753246753
0.8181818182x + x2 = 1.753246753

The x term is 0.8181818182x.  Take half its coefficient (0.4090909091).
Square it (0.1673553719) and add it to both sides.

Add '0.1673553719' to each side of the equation.
0.8181818182x + 0.1673553719 + x2 = 1.753246753 + 0.1673553719

Reorder the terms:
0.1673553719 + 0.8181818182x + x2 = 1.753246753 + 0.1673553719

Combine like terms: 1.753246753 + 0.1673553719 = 1.9206021249
0.1673553719 + 0.8181818182x + x2 = 1.9206021249

Factor a perfect square on the left side:
(x + 0.4090909091)(x + 0.4090909091) = 1.9206021249

Calculate the square root of the right side: 1.385857902

Break this problem into two subproblems by setting 
(x + 0.4090909091) equal to 1.385857902 and -1.385857902.

Subproblem 1

x + 0.4090909091 = 1.385857902 Simplifying x + 0.4090909091 = 1.385857902 Reorder the terms: 0.4090909091 + x = 1.385857902 Solving 0.4090909091 + x = 1.385857902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = 1.385857902 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = 1.385857902 + -0.4090909091 x = 1.385857902 + -0.4090909091 Combine like terms: 1.385857902 + -0.4090909091 = 0.9767669929 x = 0.9767669929 Simplifying x = 0.9767669929

Subproblem 2

x + 0.4090909091 = -1.385857902 Simplifying x + 0.4090909091 = -1.385857902 Reorder the terms: 0.4090909091 + x = -1.385857902 Solving 0.4090909091 + x = -1.385857902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = -1.385857902 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = -1.385857902 + -0.4090909091 x = -1.385857902 + -0.4090909091 Combine like terms: -1.385857902 + -0.4090909091 = -1.7949488111 x = -1.7949488111 Simplifying x = -1.7949488111

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9767669929, -1.7949488111}

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