8x(6x+7)=7

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Solution for 8x(6x+7)=7 equation:


Simplifying
8x(6x + 7) = 7

Reorder the terms:
8x(7 + 6x) = 7
(7 * 8x + 6x * 8x) = 7
(56x + 48x2) = 7

Solving
56x + 48x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 56x + 48x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 56x + 48x2 = 0

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

Divide each side by '48'.
-0.1458333333 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '0.1458333333' to each side of the equation.
-0.1458333333 + 1.166666667x + 0.1458333333 + x2 = 0 + 0.1458333333

Reorder the terms:
-0.1458333333 + 0.1458333333 + 1.166666667x + x2 = 0 + 0.1458333333

Combine like terms: -0.1458333333 + 0.1458333333 = 0.0000000000
0.0000000000 + 1.166666667x + x2 = 0 + 0.1458333333
1.166666667x + x2 = 0 + 0.1458333333

Combine like terms: 0 + 0.1458333333 = 0.1458333333
1.166666667x + x2 = 0.1458333333

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = 0.1458333333 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = 0.1458333333 + 0.3402777780

Combine like terms: 0.1458333333 + 0.3402777780 = 0.4861111113
0.3402777780 + 1.166666667x + x2 = 0.4861111113

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 0.4861111113

Calculate the square root of the right side: 0.697216689

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 0.697216689 and -0.697216689.

Subproblem 1

x + 0.5833333335 = 0.697216689 Simplifying x + 0.5833333335 = 0.697216689 Reorder the terms: 0.5833333335 + x = 0.697216689 Solving 0.5833333335 + x = 0.697216689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 0.697216689 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.697216689 + -0.5833333335 x = 0.697216689 + -0.5833333335 Combine like terms: 0.697216689 + -0.5833333335 = 0.1138833555 x = 0.1138833555 Simplifying x = 0.1138833555

Subproblem 2

x + 0.5833333335 = -0.697216689 Simplifying x + 0.5833333335 = -0.697216689 Reorder the terms: 0.5833333335 + x = -0.697216689 Solving 0.5833333335 + x = -0.697216689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -0.697216689 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.697216689 + -0.5833333335 x = -0.697216689 + -0.5833333335 Combine like terms: -0.697216689 + -0.5833333335 = -1.2805500225 x = -1.2805500225 Simplifying x = -1.2805500225

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1138833555, -1.2805500225}

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