5x(7x+2)-7=164

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Solution for 5x(7x+2)-7=164 equation:


Simplifying
5x(7x + 2) + -7 = 164

Reorder the terms:
5x(2 + 7x) + -7 = 164
(2 * 5x + 7x * 5x) + -7 = 164
(10x + 35x2) + -7 = 164

Reorder the terms:
-7 + 10x + 35x2 = 164

Solving
-7 + 10x + 35x2 = 164

Solving for variable 'x'.

Reorder the terms:
-7 + -164 + 10x + 35x2 = 164 + -164

Combine like terms: -7 + -164 = -171
-171 + 10x + 35x2 = 164 + -164

Combine like terms: 164 + -164 = 0
-171 + 10x + 35x2 = 0

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

Divide each side by '35'.
-4.885714286 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '4.885714286' to each side of the equation.
-4.885714286 + 0.2857142857x + 4.885714286 + x2 = 0 + 4.885714286

Reorder the terms:
-4.885714286 + 4.885714286 + 0.2857142857x + x2 = 0 + 4.885714286

Combine like terms: -4.885714286 + 4.885714286 = 0.000000000
0.000000000 + 0.2857142857x + x2 = 0 + 4.885714286
0.2857142857x + x2 = 0 + 4.885714286

Combine like terms: 0 + 4.885714286 = 4.885714286
0.2857142857x + x2 = 4.885714286

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 4.885714286 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 4.885714286 + 0.02040816328

Combine like terms: 4.885714286 + 0.02040816328 = 4.90612244928
0.02040816328 + 0.2857142857x + x2 = 4.90612244928

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 4.90612244928

Calculate the square root of the right side: 2.214976851

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 2.214976851 and -2.214976851.

Subproblem 1

x + 0.1428571429 = 2.214976851 Simplifying x + 0.1428571429 = 2.214976851 Reorder the terms: 0.1428571429 + x = 2.214976851 Solving 0.1428571429 + x = 2.214976851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 2.214976851 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 2.214976851 + -0.1428571429 x = 2.214976851 + -0.1428571429 Combine like terms: 2.214976851 + -0.1428571429 = 2.0721197081 x = 2.0721197081 Simplifying x = 2.0721197081

Subproblem 2

x + 0.1428571429 = -2.214976851 Simplifying x + 0.1428571429 = -2.214976851 Reorder the terms: 0.1428571429 + x = -2.214976851 Solving 0.1428571429 + x = -2.214976851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -2.214976851 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -2.214976851 + -0.1428571429 x = -2.214976851 + -0.1428571429 Combine like terms: -2.214976851 + -0.1428571429 = -2.3578339939 x = -2.3578339939 Simplifying x = -2.3578339939

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.0721197081, -2.3578339939}

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