3x(x+4)=-x+8

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


Simplifying
3x(x + 4) = -1x + 8

Reorder the terms:
3x(4 + x) = -1x + 8
(4 * 3x + x * 3x) = -1x + 8
(12x + 3x2) = -1x + 8

Reorder the terms:
12x + 3x2 = 8 + -1x

Solving
12x + 3x2 = 8 + -1x

Solving for variable 'x'.

Reorder the terms:
-8 + 12x + x + 3x2 = 8 + -1x + -8 + x

Combine like terms: 12x + x = 13x
-8 + 13x + 3x2 = 8 + -1x + -8 + x

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

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

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

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

Divide each side by '3'.
-2.666666667 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 4.333333333x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 4.333333333x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 2.666666667
4.333333333x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
4.333333333x + x2 = 2.666666667

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 = 2.666666667 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 2.666666667 + 4.694444446

Combine like terms: 2.666666667 + 4.694444446 = 7.361111113
4.694444446 + 4.333333333x + x2 = 7.361111113

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 7.361111113

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.713136766 and -2.713136766.

Subproblem 1

x + 2.166666667 = 2.713136766 Simplifying x + 2.166666667 = 2.713136766 Reorder the terms: 2.166666667 + x = 2.713136766 Solving 2.166666667 + x = 2.713136766 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 = 2.713136766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 2.713136766 + -2.166666667 x = 2.713136766 + -2.166666667 Combine like terms: 2.713136766 + -2.166666667 = 0.546470099 x = 0.546470099 Simplifying x = 0.546470099

Subproblem 2

x + 2.166666667 = -2.713136766 Simplifying x + 2.166666667 = -2.713136766 Reorder the terms: 2.166666667 + x = -2.713136766 Solving 2.166666667 + x = -2.713136766 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 = -2.713136766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -2.713136766 + -2.166666667 x = -2.713136766 + -2.166666667 Combine like terms: -2.713136766 + -2.166666667 = -4.879803433 x = -4.879803433 Simplifying x = -4.879803433

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.546470099, -4.879803433}

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