x+x(x+54)=180

Simple and best practice solution for x+x(x+54)=180 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 x+x(x+54)=180 equation:


Simplifying
x + x(x + 54) = 180

Reorder the terms:
x + x(54 + x) = 180
x + (54 * x + x * x) = 180
x + (54x + x2) = 180

Combine like terms: x + 54x = 55x
55x + x2 = 180

Solving
55x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 55x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 55x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 55x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 55x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 55x + x2 = 0 + 180
55x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
55x + x2 = 180

The x term is 55x.  Take half its coefficient (27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
55x + 756.25 + x2 = 180 + 756.25

Reorder the terms:
756.25 + 55x + x2 = 180 + 756.25

Combine like terms: 180 + 756.25 = 936.25
756.25 + 55x + x2 = 936.25

Factor a perfect square on the left side:
(x + 27.5)(x + 27.5) = 936.25

Calculate the square root of the right side: 30.598202562

Break this problem into two subproblems by setting 
(x + 27.5) equal to 30.598202562 and -30.598202562.

Subproblem 1

x + 27.5 = 30.598202562 Simplifying x + 27.5 = 30.598202562 Reorder the terms: 27.5 + x = 30.598202562 Solving 27.5 + x = 30.598202562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 30.598202562 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 30.598202562 + -27.5 x = 30.598202562 + -27.5 Combine like terms: 30.598202562 + -27.5 = 3.098202562 x = 3.098202562 Simplifying x = 3.098202562

Subproblem 2

x + 27.5 = -30.598202562 Simplifying x + 27.5 = -30.598202562 Reorder the terms: 27.5 + x = -30.598202562 Solving 27.5 + x = -30.598202562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -30.598202562 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -30.598202562 + -27.5 x = -30.598202562 + -27.5 Combine like terms: -30.598202562 + -27.5 = -58.098202562 x = -58.098202562 Simplifying x = -58.098202562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.098202562, -58.098202562}

See similar equations:

| -5x-6=3(x+4)+6 | | -t+30=5t | | 5p^2+25p+30=0 | | 8+(-2n+2)=-3(4n-7)+5 | | 2x^3+5x^2-4x-3=0 | | x+0.5x=189 | | 2.9(z+0.5)=-2.9(z-16) | | x-0.9x=56 | | 9y=-3y+36 | | 5(x-3)-2x=-3(x+5)+6x | | 8(x-4)+5x=4(x-8)+9x | | 8a+4.6=17(a-1) | | x^2+10x=-50 | | 8-1+4.6=17 | | 4(x-4)=3(6+2x)-2x | | 8*-1+4.6=17 | | 3(x+2)=8x+5-5x+1 | | 7x-8=7(x+1) | | 6.1+5.8x=x+80.3 | | 0.6(x+200)=0.66x-306 | | 7-3(3y-7)=-2(-8y+8)-6 | | 11(x+4)-4(x-4)=4(x-1)+2(x-4) | | -7s+15=15 | | 4-5(-4n+8)=-3(3n-4)-2 | | 10x+52=22 | | -7c+2=-19 | | 5(4x-7)-7=5(x-3)+78 | | -4w-5=-2w+1 | | 4x^2-23x+20=-8x+6 | | -x^2+3x+2=0 | | 4x+3=3x-6 | | 9s+4s= |

Equations solver categories