3x*(7-x)=7-8x

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Solution for 3x*(7-x)=7-8x equation:


Simplifying
3x(7 + -1x) = 7 + -8x
(7 * 3x + -1x * 3x) = 7 + -8x
(21x + -3x2) = 7 + -8x

Solving
21x + -3x2 = 7 + -8x

Solving for variable 'x'.

Reorder the terms:
-7 + 21x + 8x + -3x2 = 7 + -8x + -7 + 8x

Combine like terms: 21x + 8x = 29x
-7 + 29x + -3x2 = 7 + -8x + -7 + 8x

Reorder the terms:
-7 + 29x + -3x2 = 7 + -7 + -8x + 8x

Combine like terms: 7 + -7 = 0
-7 + 29x + -3x2 = 0 + -8x + 8x
-7 + 29x + -3x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-7 + 29x + -3x2 = 0

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

Divide each side by '-3'.
2.333333333 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -9.666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -9.666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -9.666666667x + x2 = 0 + -2.333333333
-9.666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-9.666666667x + x2 = -2.333333333

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = -2.333333333 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = -2.333333333 + 23.36111112

Combine like terms: -2.333333333 + 23.36111112 = 21.027777787
23.36111112 + -9.666666667x + x2 = 21.027777787

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 21.027777787

Calculate the square root of the right side: 4.585605498

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 4.585605498 and -4.585605498.

Subproblem 1

x + -4.833333334 = 4.585605498 Simplifying x + -4.833333334 = 4.585605498 Reorder the terms: -4.833333334 + x = 4.585605498 Solving -4.833333334 + x = 4.585605498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 4.585605498 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 4.585605498 + 4.833333334 x = 4.585605498 + 4.833333334 Combine like terms: 4.585605498 + 4.833333334 = 9.418938832 x = 9.418938832 Simplifying x = 9.418938832

Subproblem 2

x + -4.833333334 = -4.585605498 Simplifying x + -4.833333334 = -4.585605498 Reorder the terms: -4.833333334 + x = -4.585605498 Solving -4.833333334 + x = -4.585605498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -4.585605498 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -4.585605498 + 4.833333334 x = -4.585605498 + 4.833333334 Combine like terms: -4.585605498 + 4.833333334 = 0.247727836 x = 0.247727836 Simplifying x = 0.247727836

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.418938832, 0.247727836}

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