x^2-6x=0.5x+42

Simple and best practice solution for x^2-6x=0.5x+42 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^2-6x=0.5x+42 equation:


Simplifying
x2 + -6x = 0.5x + 42

Reorder the terms:
-6x + x2 = 0.5x + 42

Reorder the terms:
-6x + x2 = 42 + 0.5x

Solving
-6x + x2 = 42 + 0.5x

Solving for variable 'x'.

Reorder the terms:
-42 + -6x + -0.5x + x2 = 42 + 0.5x + -42 + -0.5x

Combine like terms: -6x + -0.5x = -6.5x
-42 + -6.5x + x2 = 42 + 0.5x + -42 + -0.5x

Reorder the terms:
-42 + -6.5x + x2 = 42 + -42 + 0.5x + -0.5x

Combine like terms: 42 + -42 = 0
-42 + -6.5x + x2 = 0 + 0.5x + -0.5x
-42 + -6.5x + x2 = 0.5x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
-42 + -6.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -6.5x + 42 + x2 = 0.0 + 42

Reorder the terms:
-42 + 42 + -6.5x + x2 = 0.0 + 42

Combine like terms: -42 + 42 = 0
0 + -6.5x + x2 = 0.0 + 42
-6.5x + x2 = 0.0 + 42

Combine like terms: 0.0 + 42 = 42
-6.5x + x2 = 42

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 42 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 42 + 10.5625

Combine like terms: 42 + 10.5625 = 52.5625
10.5625 + -6.5x + x2 = 52.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 52.5625

Calculate the square root of the right side: 7.25

Break this problem into two subproblems by setting 
(x + -3.25) equal to 7.25 and -7.25.

Subproblem 1

x + -3.25 = 7.25 Simplifying x + -3.25 = 7.25 Reorder the terms: -3.25 + x = 7.25 Solving -3.25 + x = 7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 7.25 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 7.25 + 3.25 x = 7.25 + 3.25 Combine like terms: 7.25 + 3.25 = 10.5 x = 10.5 Simplifying x = 10.5

Subproblem 2

x + -3.25 = -7.25 Simplifying x + -3.25 = -7.25 Reorder the terms: -3.25 + x = -7.25 Solving -3.25 + x = -7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -7.25 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -7.25 + 3.25 x = -7.25 + 3.25 Combine like terms: -7.25 + 3.25 = -4 x = -4 Simplifying x = -4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.5, -4}

See similar equations:

| 16-5x=1-24x | | X-2(7x-1)=-12x-1 | | 21-G=9.5 | | x+115=6x | | 5x-4=6x-7 | | 150m-100m+43875=45225-175m | | 3(2x+1)=56 | | 15-a=45 | | x+6=3x-32 | | x^2-6.5x-52=0 | | 12x+5=8x-15 | | (9b-27)=21 | | 4.4m+6.2=8.8m-88 | | -3x+2(2+3x)=5x+8 | | -3(3y-3)+9y=9 | | 3x-4=-8(x-5) | | 3(4x+5)=6(2x-4) | | 7x-2-3=4(x+10) | | 44=5r+19-4r | | r+26-3r=54 | | 5x+4x+20=180 | | 12(4x+5)=6(2x+4) | | 4.5w=5.1(w-3) | | 7x+32=12-m | | 3r^2+11r+28=10(1-r) | | -22+6x=74 | | t-7+3t=33 | | 2(h+1)=5h-1 | | 27v+48=21v | | 8x-5=(-2x)-15 | | 5-35m+11m+66=4+9m+1 | | 5z+1-4z=51 |

Equations solver categories