5400=x(180-1.5x)

Simple and best practice solution for 5400=x(180-1.5x) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 5400=x(180-1.5x) equation:


Simplifying
5400 = x(180 + -1.5x)
5400 = (180 * x + -1.5x * x)
5400 = (180x + -1.5x2)

Solving
5400 = 180x + -1.5x2

Solving for variable 'x'.

Reorder the terms:
5400 + -180x + 1.5x2 = 180x + -180x + -1.5x2 + 1.5x2

Combine like terms: 180x + -180x = 0
5400 + -180x + 1.5x2 = 0 + -1.5x2 + 1.5x2
5400 + -180x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
5400 + -180x + 1.5x2 = 0.0

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

Divide each side by '1.5'.
3600 + -120x + x2 = 0

Move the constant term to the right:

Add '-3600' to each side of the equation.
3600 + -120x + -3600 + x2 = 0 + -3600

Reorder the terms:
3600 + -3600 + -120x + x2 = 0 + -3600

Combine like terms: 3600 + -3600 = 0
0 + -120x + x2 = 0 + -3600
-120x + x2 = 0 + -3600

Combine like terms: 0 + -3600 = -3600
-120x + x2 = -3600

The x term is -120x.  Take half its coefficient (-60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
-120x + 3600 + x2 = -3600 + 3600

Reorder the terms:
3600 + -120x + x2 = -3600 + 3600

Combine like terms: -3600 + 3600 = 0
3600 + -120x + x2 = 0

Factor a perfect square on the left side:
(x + -60)(x + -60) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -60) equal to 0 and 0.

Subproblem 1

x + -60 = 0 Simplifying x + -60 = 0 Reorder the terms: -60 + x = 0 Solving -60 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 0 + 60 Combine like terms: -60 + 60 = 0 0 + x = 0 + 60 x = 0 + 60 Combine like terms: 0 + 60 = 60 x = 60 Simplifying x = 60

Subproblem 2

x + -60 = 0 Simplifying x + -60 = 0 Reorder the terms: -60 + x = 0 Solving -60 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 0 + 60 Combine like terms: -60 + 60 = 0 0 + x = 0 + 60 x = 0 + 60 Combine like terms: 0 + 60 = 60 x = 60 Simplifying x = 60

Solution

The solution to the problem is based on the solutions from the subproblems. x = {60, 60}

See similar equations:

| -7n+8=-3n-16 | | 0.65x+0.05(2-x)=0.10(-47) | | (7x-3)(4x^2-6x+4)=0 | | -x^2-3x-4=0 | | 2x-1=70 | | -3=3x-13 | | 7/6x=120 | | 2x-8=180/3 | | 70=x-13 | | x-13=70 | | 0.20x+0.05(12-x)=0.10(0) | | 6x+7=5x+8 | | (1−x)^(1/3)−0.11−1/3x | | 36-(18-x)+(18-x)= | | 2x+4+4x-4=180 | | x^3+50x+625=0 | | (6m-1)(m^2-7m-1)=0 | | 6x+2x+10=90 | | Y=1/2(12) | | -4.9t^2+15t+100=0 | | 8X+6=40 | | 3x-1=16/2 | | (49x^4)1/2 | | 90+50+x=180 | | (-2/1/7)p=-3 | | 6+78=39x+9 | | 5x-8x-3x+7x^2= | | 7(12-2x)=4(3-3x) | | -2.4p=-7.2 | | 9p^2-24p+72=0 | | 3p+q=p | | 5/6r-1/6=4 |

Equations solver categories