5x+32=-3x(x-24)

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Solution for 5x+32=-3x(x-24) equation:


Simplifying
5x + 32 = -3x(x + -24)

Reorder the terms:
32 + 5x = -3x(x + -24)

Reorder the terms:
32 + 5x = -3x(-24 + x)
32 + 5x = (-24 * -3x + x * -3x)
32 + 5x = (72x + -3x2)

Solving
32 + 5x = 72x + -3x2

Solving for variable 'x'.

Combine like terms: 5x + -72x = -67x
32 + -67x + 3x2 = 72x + -3x2 + -72x + 3x2

Reorder the terms:
32 + -67x + 3x2 = 72x + -72x + -3x2 + 3x2

Combine like terms: 72x + -72x = 0
32 + -67x + 3x2 = 0 + -3x2 + 3x2
32 + -67x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
32 + -67x + 3x2 = 0

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

Divide each side by '3'.
10.66666667 + -22.33333333x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + -22.33333333x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + -22.33333333x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + -22.33333333x + x2 = 0 + -10.66666667
-22.33333333x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
-22.33333333x + x2 = -10.66666667

The x term is -22.33333333x.  Take half its coefficient (-11.16666667).
Square it (124.6944445) and add it to both sides.

Add '124.6944445' to each side of the equation.
-22.33333333x + 124.6944445 + x2 = -10.66666667 + 124.6944445

Reorder the terms:
124.6944445 + -22.33333333x + x2 = -10.66666667 + 124.6944445

Combine like terms: -10.66666667 + 124.6944445 = 114.02777783
124.6944445 + -22.33333333x + x2 = 114.02777783

Factor a perfect square on the left side:
(x + -11.16666667)(x + -11.16666667) = 114.02777783

Calculate the square root of the right side: 10.678378989

Break this problem into two subproblems by setting 
(x + -11.16666667) equal to 10.678378989 and -10.678378989.

Subproblem 1

x + -11.16666667 = 10.678378989 Simplifying x + -11.16666667 = 10.678378989 Reorder the terms: -11.16666667 + x = 10.678378989 Solving -11.16666667 + x = 10.678378989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.16666667' to each side of the equation. -11.16666667 + 11.16666667 + x = 10.678378989 + 11.16666667 Combine like terms: -11.16666667 + 11.16666667 = 0.00000000 0.00000000 + x = 10.678378989 + 11.16666667 x = 10.678378989 + 11.16666667 Combine like terms: 10.678378989 + 11.16666667 = 21.845045659 x = 21.845045659 Simplifying x = 21.845045659

Subproblem 2

x + -11.16666667 = -10.678378989 Simplifying x + -11.16666667 = -10.678378989 Reorder the terms: -11.16666667 + x = -10.678378989 Solving -11.16666667 + x = -10.678378989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.16666667' to each side of the equation. -11.16666667 + 11.16666667 + x = -10.678378989 + 11.16666667 Combine like terms: -11.16666667 + 11.16666667 = 0.00000000 0.00000000 + x = -10.678378989 + 11.16666667 x = -10.678378989 + 11.16666667 Combine like terms: -10.678378989 + 11.16666667 = 0.488287681 x = 0.488287681 Simplifying x = 0.488287681

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.845045659, 0.488287681}

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