(8x-7)*6x=73

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Solution for (8x-7)*6x=73 equation:


Simplifying
(8x + -7) * 6x = 73

Reorder the terms:
(-7 + 8x) * 6x = 73

Reorder the terms for easier multiplication:
6x(-7 + 8x) = 73
(-7 * 6x + 8x * 6x) = 73
(-42x + 48x2) = 73

Solving
-42x + 48x2 = 73

Solving for variable 'x'.

Reorder the terms:
-73 + -42x + 48x2 = 73 + -73

Combine like terms: 73 + -73 = 0
-73 + -42x + 48x2 = 0

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

Divide each side by '48'.
-1.520833333 + -0.875x + x2 = 0

Move the constant term to the right:

Add '1.520833333' to each side of the equation.
-1.520833333 + -0.875x + 1.520833333 + x2 = 0 + 1.520833333

Reorder the terms:
-1.520833333 + 1.520833333 + -0.875x + x2 = 0 + 1.520833333

Combine like terms: -1.520833333 + 1.520833333 = 0.000000000
0.000000000 + -0.875x + x2 = 0 + 1.520833333
-0.875x + x2 = 0 + 1.520833333

Combine like terms: 0 + 1.520833333 = 1.520833333
-0.875x + x2 = 1.520833333

The x term is -0.875x.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875x + 0.19140625 + x2 = 1.520833333 + 0.19140625

Reorder the terms:
0.19140625 + -0.875x + x2 = 1.520833333 + 0.19140625

Combine like terms: 1.520833333 + 0.19140625 = 1.712239583
0.19140625 + -0.875x + x2 = 1.712239583

Factor a perfect square on the left side:
(x + -0.4375)(x + -0.4375) = 1.712239583

Calculate the square root of the right side: 1.308525729

Break this problem into two subproblems by setting 
(x + -0.4375) equal to 1.308525729 and -1.308525729.

Subproblem 1

x + -0.4375 = 1.308525729 Simplifying x + -0.4375 = 1.308525729 Reorder the terms: -0.4375 + x = 1.308525729 Solving -0.4375 + x = 1.308525729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 1.308525729 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 1.308525729 + 0.4375 x = 1.308525729 + 0.4375 Combine like terms: 1.308525729 + 0.4375 = 1.746025729 x = 1.746025729 Simplifying x = 1.746025729

Subproblem 2

x + -0.4375 = -1.308525729 Simplifying x + -0.4375 = -1.308525729 Reorder the terms: -0.4375 + x = -1.308525729 Solving -0.4375 + x = -1.308525729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -1.308525729 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -1.308525729 + 0.4375 x = -1.308525729 + 0.4375 Combine like terms: -1.308525729 + 0.4375 = -0.871025729 x = -0.871025729 Simplifying x = -0.871025729

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.746025729, -0.871025729}

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