45x+x^2=500

Simple and best practice solution for 45x+x^2=500 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 45x+x^2=500 equation:


Simplifying
45x + x2 = 500

Solving
45x + x2 = 500

Solving for variable 'x'.

Reorder the terms:
-500 + 45x + x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 45x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 45x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 45x + x2 = 0 + 500
45x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
45x + x2 = 500

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 500 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 500 + 506.25

Combine like terms: 500 + 506.25 = 1006.25
506.25 + 45x + x2 = 1006.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 1006.25

Calculate the square root of the right side: 31.721443851

Break this problem into two subproblems by setting 
(x + 22.5) equal to 31.721443851 and -31.721443851.

Subproblem 1

x + 22.5 = 31.721443851 Simplifying x + 22.5 = 31.721443851 Reorder the terms: 22.5 + x = 31.721443851 Solving 22.5 + x = 31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 31.721443851 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 31.721443851 + -22.5 x = 31.721443851 + -22.5 Combine like terms: 31.721443851 + -22.5 = 9.221443851 x = 9.221443851 Simplifying x = 9.221443851

Subproblem 2

x + 22.5 = -31.721443851 Simplifying x + 22.5 = -31.721443851 Reorder the terms: 22.5 + x = -31.721443851 Solving 22.5 + x = -31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -31.721443851 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -31.721443851 + -22.5 x = -31.721443851 + -22.5 Combine like terms: -31.721443851 + -22.5 = -54.221443851 x = -54.221443851 Simplifying x = -54.221443851

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.221443851, -54.221443851}

See similar equations:

| 1nx=-4 | | 15=-3.8t+45 | | 4x/5-2=14 | | -4(-3)-5= | | 10+0.10t=0.35t | | 80-c=60 | | g(x)=log(0.4x) | | 5x(3x+3)=3 | | x+17=5x-2 | | (6/e^3x) | | 31+3z=-2(7z+6) | | ln(x^2)=-1/2 | | Y1/3x-5 | | 68-az=5x | | 3x+48=5x+24 | | n+0.08n= | | X+(y+71)=351 | | 5n^2-33n+18=0 | | b^2-c^3+d^4= | | 8st=264 | | 2x^2-18=14 | | 700-d=600 | | (X+10)=(3x+20) | | 37=3u-14 | | 17x-8=3x | | 8(17-x)=16 | | 5v-11=24 | | 3*(5)^(-)*(x/4)=15 | | -5/8x=10/17 | | 16x-27=8+9x | | 36-24/3-2 | | (8y+36)=(14y-24) |

Equations solver categories