180=4x(90-x)

Simple and best practice solution for 180=4x(90-x) 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 180=4x(90-x) equation: 


Simplifying
180 = 4x(90 + -1x)
180 = (90 * 4x + -1x * 4x)
180 = (360x + -4x2)

Solving
180 = 360x + -4x2

Solving for variable 'x'.

Reorder the terms:
180 + -360x + 4x2 = 360x + -360x + -4x2 + 4x2

Combine like terms: 360x + -360x = 0
180 + -360x + 4x2 = 0 + -4x2 + 4x2
180 + -360x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
180 + -360x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -90x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(45 + -90x + x2)' equal to zero and attempt to solve:

Simplifying
45 + -90x + x2 = 0

Solving
45 + -90x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -90x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -90x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -90x + x2 = 0 + -45
-90x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-90x + x2 = -45

The x term is -90x.  Take half its coefficient (-45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
-90x + 2025 + x2 = -45 + 2025

Reorder the terms:
2025 + -90x + x2 = -45 + 2025

Combine like terms: -45 + 2025 = 1980
2025 + -90x + x2 = 1980

Factor a perfect square on the left side:
(x + -45)(x + -45) = 1980

Calculate the square root of the right side: 44.497190923

Break this problem into two subproblems by setting 
(x + -45) equal to 44.497190923 and -44.497190923.


Subproblem 1
x + -45 = 44.497190923

Simplifying
x + -45 = 44.497190923

Reorder the terms:
-45 + x = 44.497190923

Solving
-45 + x = 44.497190923

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = 44.497190923 + 45

Combine like terms: -45 + 45 = 0
0 + x = 44.497190923 + 45
x = 44.497190923 + 45

Combine like terms: 44.497190923 + 45 = 89.497190923
x = 89.497190923

Simplifying
x = 89.497190923


Subproblem 2
x + -45 = -44.497190923

Simplifying
x + -45 = -44.497190923

Reorder the terms:
-45 + x = -44.497190923

Solving
-45 + x = -44.497190923

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = -44.497190923 + 45

Combine like terms: -45 + 45 = 0
0 + x = -44.497190923 + 45
x = -44.497190923 + 45

Combine like terms: -44.497190923 + 45 = 0.502809077
x = 0.502809077

Simplifying
x = 0.502809077


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {89.497190923, 0.502809077}
Solution
x = {89.497190923, 0.502809077}

See similar equations:

| 4x-2(1-x)=-44 | | Y+4x=-4 | | x=3x(90-x)+18 | | 100+.6x=70+.9x | | 24x/3+36/3= | | (a^2+64)*(a^2+144)=1200 | | (3x+6)+(x+4)= | | 3y^7-16=-1 | | 3y^7=15 | | 2.8/0.35= | | 4r+8=18-6r | | 6(-5u+1)+7(3-2u)= | | 6(-5+1)+7(3-2u)= | | 10.8+6.4= | | 1200=(a^2+64)*(a^2+144) | | 57=3x+4y | | 13x+2x=12 | | -6.4+-10.8= | | 6y-8-2y+5=0 | | -4.1+3.6= | | 1200=(a^2+64)x(a^2+144) | | x^2+22x-48= | | 5.8+7.9= | | (a^2+64)x(a^2+144)=1200 | | (i-3)(3i+3)= | | X=2x^2+7x+5 | | F=2x^2+7x+5 | | F(x)=2x^2+7x+5 | | -4.2+6.5= | | -10+(-23)+18= | | -21+10= | | -3(n-7)+3(n-8)=n-3+8+n |

Equations solver categories