3x+4(9-x)x=7

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Solution for 3x+4(9-x)x=7 equation: 


Simplifying
3x + 4(9 + -1x) * x = 7

Reorder the terms for easier multiplication:
3x + 4x(9 + -1x) = 7
3x + (9 * 4x + -1x * 4x) = 7
3x + (36x + -4x2) = 7

Combine like terms: 3x + 36x = 39x
39x + -4x2 = 7

Solving
39x + -4x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 39x + -4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 39x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.75 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -9.75x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -9.75x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -9.75x + x2 = 0 + -1.75
-9.75x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-9.75x + x2 = -1.75

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -1.75 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -1.75 + 23.765625

Combine like terms: -1.75 + 23.765625 = 22.015625
23.765625 + -9.75x + x2 = 22.015625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 22.015625

Calculate the square root of the right side: 4.692081095

Break this problem into two subproblems by setting 
(x + -4.875) equal to 4.692081095 and -4.692081095.


Subproblem 1
x + -4.875 = 4.692081095

Simplifying
x + -4.875 = 4.692081095

Reorder the terms:
-4.875 + x = 4.692081095

Solving
-4.875 + x = 4.692081095

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = 4.692081095 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = 4.692081095 + 4.875
x = 4.692081095 + 4.875

Combine like terms: 4.692081095 + 4.875 = 9.567081095
x = 9.567081095

Simplifying
x = 9.567081095


Subproblem 2
x + -4.875 = -4.692081095

Simplifying
x + -4.875 = -4.692081095

Reorder the terms:
-4.875 + x = -4.692081095

Solving
-4.875 + x = -4.692081095

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = -4.692081095 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = -4.692081095 + 4.875
x = -4.692081095 + 4.875

Combine like terms: -4.692081095 + 4.875 = 0.182918905
x = 0.182918905

Simplifying
x = 0.182918905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.567081095, 0.182918905}

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