542=5x(100-2x)

Simple and best practice solution for 542=5x(100-2x) 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 542=5x(100-2x) equation: 


Simplifying
542 = 5x(100 + -2x)
542 = (100 * 5x + -2x * 5x)
542 = (500x + -10x2)

Solving
542 = 500x + -10x2

Solving for variable 'x'.

Reorder the terms:
542 + -500x + 10x2 = 500x + -500x + -10x2 + 10x2

Combine like terms: 500x + -500x = 0
542 + -500x + 10x2 = 0 + -10x2 + 10x2
542 + -500x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
542 + -500x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(271 + -250x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(271 + -250x + 5x2)' equal to zero and attempt to solve:

Simplifying
271 + -250x + 5x2 = 0

Solving
271 + -250x + 5x2 = 0

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

Divide each side by '5'.
54.2 + -50x + x2 = 0

Move the constant term to the right:

Add '-54.2' to each side of the equation.
54.2 + -50x + -54.2 + x2 = 0 + -54.2

Reorder the terms:
54.2 + -54.2 + -50x + x2 = 0 + -54.2

Combine like terms: 54.2 + -54.2 = 0.0
0.0 + -50x + x2 = 0 + -54.2
-50x + x2 = 0 + -54.2

Combine like terms: 0 + -54.2 = -54.2
-50x + x2 = -54.2

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -54.2 + 625

Reorder the terms:
625 + -50x + x2 = -54.2 + 625

Combine like terms: -54.2 + 625 = 570.8
625 + -50x + x2 = 570.8

Factor a perfect square on the left side:
(x + -25)(x + -25) = 570.8

Calculate the square root of the right side: 23.891421054

Break this problem into two subproblems by setting 
(x + -25) equal to 23.891421054 and -23.891421054.


Subproblem 1
x + -25 = 23.891421054

Simplifying
x + -25 = 23.891421054

Reorder the terms:
-25 + x = 23.891421054

Solving
-25 + x = 23.891421054

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + x = 23.891421054 + 25

Combine like terms: -25 + 25 = 0
0 + x = 23.891421054 + 25
x = 23.891421054 + 25

Combine like terms: 23.891421054 + 25 = 48.891421054
x = 48.891421054

Simplifying
x = 48.891421054


Subproblem 2
x + -25 = -23.891421054

Simplifying
x + -25 = -23.891421054

Reorder the terms:
-25 + x = -23.891421054

Solving
-25 + x = -23.891421054

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + x = -23.891421054 + 25

Combine like terms: -25 + 25 = 0
0 + x = -23.891421054 + 25
x = -23.891421054 + 25

Combine like terms: -23.891421054 + 25 = 1.108578946
x = 1.108578946

Simplifying
x = 1.108578946


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.891421054, 1.108578946}
Solution
x = {48.891421054, 1.108578946}

See similar equations:

| 1.428571429= | | 8x-40=8x+40 | | -9[9z-(12z+2)]=2+(2x+1) | | 15x-20=7x | | 2c=7+c | | c+3-2c-1+3c=2 | | 8(3n+6)=22-7n | | -5(-3u-6)=-3(-5u-10) | | -6(-6+6n)=3(-6n+18) | | 4(x+5)+2x=32 | | 8/3/24/5 | | -4+x=3x-2 | | 32x=120 | | 8x+12y=180 | | 13-2(3w-1)=31 | | 5x-5=150 | | -4(6-12m)=-3(-18m-8) | | 15/5/11 | | 7/8x-9/8=4 | | 65=m(5) | | 28=-6+5(s-4) | | -10+6x=3x+14 | | -6(-16)+3+4(-16)=-16+19 | | x+39=350 | | 4/6x+8=32 | | 5(-3u-14)=-15-10u | | 5/7/25 | | 4+5m=65 | | 17=4a+5a | | -18.2b-10.71=-17.5b | | 3x-(4x+3)=0 | | 8/4=a/6 |

Equations solver categories