7x-3(9-7x)x=-1

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Solution for 7x-3(9-7x)x=-1 equation:


Simplifying
7x + -3(9 + -7x) * x = -1

Reorder the terms for easier multiplication:
7x + -3x(9 + -7x) = -1
7x + (9 * -3x + -7x * -3x) = -1
7x + (-27x + 21x2) = -1

Combine like terms: 7x + -27x = -20x
-20x + 21x2 = -1

Solving
-20x + 21x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -20x + 21x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -20x + 21x2 = 0

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

Divide each side by '21'.
0.04761904762 + -0.9523809524x + x2 = 0

Move the constant term to the right:

Add '-0.04761904762' to each side of the equation.
0.04761904762 + -0.9523809524x + -0.04761904762 + x2 = 0 + -0.04761904762

Reorder the terms:
0.04761904762 + -0.04761904762 + -0.9523809524x + x2 = 0 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + -0.9523809524x + x2 = 0 + -0.04761904762
-0.9523809524x + x2 = 0 + -0.04761904762

Combine like terms: 0 + -0.04761904762 = -0.04761904762
-0.9523809524x + x2 = -0.04761904762

The x term is -0.9523809524x.  Take half its coefficient (-0.4761904762).
Square it (0.2267573696) and add it to both sides.

Add '0.2267573696' to each side of the equation.
-0.9523809524x + 0.2267573696 + x2 = -0.04761904762 + 0.2267573696

Reorder the terms:
0.2267573696 + -0.9523809524x + x2 = -0.04761904762 + 0.2267573696

Combine like terms: -0.04761904762 + 0.2267573696 = 0.17913832198
0.2267573696 + -0.9523809524x + x2 = 0.17913832198

Factor a perfect square on the left side:
(x + -0.4761904762)(x + -0.4761904762) = 0.17913832198

Calculate the square root of the right side: 0.423247353

Break this problem into two subproblems by setting 
(x + -0.4761904762) equal to 0.423247353 and -0.423247353.

Subproblem 1

x + -0.4761904762 = 0.423247353 Simplifying x + -0.4761904762 = 0.423247353 Reorder the terms: -0.4761904762 + x = 0.423247353 Solving -0.4761904762 + x = 0.423247353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = 0.423247353 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = 0.423247353 + 0.4761904762 x = 0.423247353 + 0.4761904762 Combine like terms: 0.423247353 + 0.4761904762 = 0.8994378292 x = 0.8994378292 Simplifying x = 0.8994378292

Subproblem 2

x + -0.4761904762 = -0.423247353 Simplifying x + -0.4761904762 = -0.423247353 Reorder the terms: -0.4761904762 + x = -0.423247353 Solving -0.4761904762 + x = -0.423247353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = -0.423247353 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = -0.423247353 + 0.4761904762 x = -0.423247353 + 0.4761904762 Combine like terms: -0.423247353 + 0.4761904762 = 0.0529431232 x = 0.0529431232 Simplifying x = 0.0529431232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8994378292, 0.0529431232}

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