120x=500+x^2

Simple and best practice solution for 120x=500+x^2 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 120x=500+x^2 equation:


Simplifying
120x = 500 + x2

Solving
120x = 500 + x2

Solving for variable 'x'.

Reorder the terms:
-500 + 120x + -1x2 = 500 + x2 + -500 + -1x2

Reorder the terms:
-500 + 120x + -1x2 = 500 + -500 + x2 + -1x2

Combine like terms: 500 + -500 = 0
-500 + 120x + -1x2 = 0 + x2 + -1x2
-500 + 120x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-500 + 120x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
500 + -120x + x2 = 0

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + -120x + -500 + x2 = 0 + -500

Reorder the terms:
500 + -500 + -120x + x2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -120x + x2 = 0 + -500
-120x + x2 = 0 + -500

Combine like terms: 0 + -500 = -500
-120x + x2 = -500

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 = -500 + 3600

Reorder the terms:
3600 + -120x + x2 = -500 + 3600

Combine like terms: -500 + 3600 = 3100
3600 + -120x + x2 = 3100

Factor a perfect square on the left side:
(x + -60)(x + -60) = 3100

Calculate the square root of the right side: 55.677643628

Break this problem into two subproblems by setting 
(x + -60) equal to 55.677643628 and -55.677643628.

Subproblem 1

x + -60 = 55.677643628 Simplifying x + -60 = 55.677643628 Reorder the terms: -60 + x = 55.677643628 Solving -60 + x = 55.677643628 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 = 55.677643628 + 60 Combine like terms: -60 + 60 = 0 0 + x = 55.677643628 + 60 x = 55.677643628 + 60 Combine like terms: 55.677643628 + 60 = 115.677643628 x = 115.677643628 Simplifying x = 115.677643628

Subproblem 2

x + -60 = -55.677643628 Simplifying x + -60 = -55.677643628 Reorder the terms: -60 + x = -55.677643628 Solving -60 + x = -55.677643628 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 = -55.677643628 + 60 Combine like terms: -60 + 60 = 0 0 + x = -55.677643628 + 60 x = -55.677643628 + 60 Combine like terms: -55.677643628 + 60 = 4.322356372 x = 4.322356372 Simplifying x = 4.322356372

Solution

The solution to the problem is based on the solutions from the subproblems. x = {115.677643628, 4.322356372}

See similar equations:

| 12x+21=3x+174 | | 13=-5x-12 | | 2x-5sqrt(x)-7=0 | | -32=-4/3xs | | 5y/2y=10 | | x+10+z=8 | | 5(3-k)+2(3-k)=14 | | (2m^2+5m+11)(2m^2+5m+1)=-9 | | -8x+2x=-16+16x | | 3x+4=11x-5(x-7) | | 42=-6(2x-3) | | sin(3x)=5 | | 4y-z=20 | | 4x+33=5x-7 | | -5x+5x+1+5x-1=21 | | (X-1/6)^10 | | 2x-19=6x+10 | | 3x-9=27x+8 | | 4=3u+7 | | 20-(4x+3y)= | | 56=28+14(x-12) | | Log[2](7x+3)=4 | | (3x)+(3x)+(2x)=180 | | 15=2g+5k | | -9x=2.6 | | 2/7y-3=11 | | x+2y=8-z | | 45=3k+9 | | 1/(8ln8) | | 39/24= | | 2(x-1)-3=-3(-x+5)-2x | | 6.4-2.2x+3.4x=-4.4 |

Equations solver categories