71-(3x+15)=3x(x+7)+x

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Solution for 71-(3x+15)=3x(x+7)+x equation:


Simplifying
71 + -1(3x + 15) = 3x(x + 7) + x

Reorder the terms:
71 + -1(15 + 3x) = 3x(x + 7) + x
71 + (15 * -1 + 3x * -1) = 3x(x + 7) + x
71 + (-15 + -3x) = 3x(x + 7) + x

Combine like terms: 71 + -15 = 56
56 + -3x = 3x(x + 7) + x

Reorder the terms:
56 + -3x = 3x(7 + x) + x
56 + -3x = (7 * 3x + x * 3x) + x
56 + -3x = (21x + 3x2) + x

Reorder the terms:
56 + -3x = 21x + x + 3x2

Combine like terms: 21x + x = 22x
56 + -3x = 22x + 3x2

Solving
56 + -3x = 22x + 3x2

Solving for variable 'x'.

Combine like terms: -3x + -22x = -25x
56 + -25x + -3x2 = 22x + 3x2 + -22x + -3x2

Reorder the terms:
56 + -25x + -3x2 = 22x + -22x + 3x2 + -3x2

Combine like terms: 22x + -22x = 0
56 + -25x + -3x2 = 0 + 3x2 + -3x2
56 + -25x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
56 + -25x + -3x2 = 0

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

Divide each side by '-3'.
-18.66666667 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + 8.333333333x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + 8.333333333x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + 8.333333333x + x2 = 0 + 18.66666667
8.333333333x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
8.333333333x + x2 = 18.66666667

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 18.66666667 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 18.66666667 + 17.36111111

Combine like terms: 18.66666667 + 17.36111111 = 36.02777778
17.36111111 + 8.333333333x + x2 = 36.02777778

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 36.02777778

Calculate the square root of the right side: 6.002314369

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 6.002314369 and -6.002314369.

Subproblem 1

x + 4.166666667 = 6.002314369 Simplifying x + 4.166666667 = 6.002314369 Reorder the terms: 4.166666667 + x = 6.002314369 Solving 4.166666667 + x = 6.002314369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 6.002314369 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 6.002314369 + -4.166666667 x = 6.002314369 + -4.166666667 Combine like terms: 6.002314369 + -4.166666667 = 1.835647702 x = 1.835647702 Simplifying x = 1.835647702

Subproblem 2

x + 4.166666667 = -6.002314369 Simplifying x + 4.166666667 = -6.002314369 Reorder the terms: 4.166666667 + x = -6.002314369 Solving 4.166666667 + x = -6.002314369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -6.002314369 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -6.002314369 + -4.166666667 x = -6.002314369 + -4.166666667 Combine like terms: -6.002314369 + -4.166666667 = -10.168981036 x = -10.168981036 Simplifying x = -10.168981036

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.835647702, -10.168981036}

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