4x-1x(9-3x)=8x-1

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Solution for 4x-1x(9-3x)=8x-1 equation:


Simplifying
4x + -1x(9 + -3x) = 8x + -1
4x + (9 * -1x + -3x * -1x) = 8x + -1
4x + (-9x + 3x2) = 8x + -1

Combine like terms: 4x + -9x = -5x
-5x + 3x2 = 8x + -1

Reorder the terms:
-5x + 3x2 = -1 + 8x

Solving
-5x + 3x2 = -1 + 8x

Solving for variable 'x'.

Reorder the terms:
1 + -5x + -8x + 3x2 = -1 + 8x + 1 + -8x

Combine like terms: -5x + -8x = -13x
1 + -13x + 3x2 = -1 + 8x + 1 + -8x

Reorder the terms:
1 + -13x + 3x2 = -1 + 1 + 8x + -8x

Combine like terms: -1 + 1 = 0
1 + -13x + 3x2 = 0 + 8x + -8x
1 + -13x + 3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
1 + -13x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -4.333333333x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -4.333333333x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -4.333333333x + x2 = 0 + -0.3333333333
-4.333333333x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-4.333333333x + x2 = -0.3333333333

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -0.3333333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -0.3333333333 + 4.694444446

Combine like terms: -0.3333333333 + 4.694444446 = 4.3611111127
4.694444446 + -4.333333333x + x2 = 4.3611111127

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 4.3611111127

Calculate the square root of the right side: 2.088327348

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 2.088327348 and -2.088327348.

Subproblem 1

x + -2.166666667 = 2.088327348 Simplifying x + -2.166666667 = 2.088327348 Reorder the terms: -2.166666667 + x = 2.088327348 Solving -2.166666667 + x = 2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 2.088327348 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.088327348 + 2.166666667 x = 2.088327348 + 2.166666667 Combine like terms: 2.088327348 + 2.166666667 = 4.254994015 x = 4.254994015 Simplifying x = 4.254994015

Subproblem 2

x + -2.166666667 = -2.088327348 Simplifying x + -2.166666667 = -2.088327348 Reorder the terms: -2.166666667 + x = -2.088327348 Solving -2.166666667 + x = -2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -2.088327348 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.088327348 + 2.166666667 x = -2.088327348 + 2.166666667 Combine like terms: -2.088327348 + 2.166666667 = 0.078339319 x = 0.078339319 Simplifying x = 0.078339319

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.254994015, 0.078339319}

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