x^2-24x+144=108

Simple and best practice solution for x^2-24x+144=108 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^2-24x+144=108 equation:


Simplifying
x2 + -24x + 144 = 108

Reorder the terms:
144 + -24x + x2 = 108

Solving
144 + -24x + x2 = 108

Solving for variable 'x'.

Reorder the terms:
144 + -108 + -24x + x2 = 108 + -108

Combine like terms: 144 + -108 = 36
36 + -24x + x2 = 108 + -108

Combine like terms: 108 + -108 = 0
36 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -24x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -24x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -24x + x2 = 0 + -36
-24x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-24x + x2 = -36

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -36 + 144

Reorder the terms:
144 + -24x + x2 = -36 + 144

Combine like terms: -36 + 144 = 108
144 + -24x + x2 = 108

Factor a perfect square on the left side:
(x + -12)(x + -12) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x + -12) equal to 10.392304845 and -10.392304845.

Subproblem 1

x + -12 = 10.392304845 Simplifying x + -12 = 10.392304845 Reorder the terms: -12 + x = 10.392304845 Solving -12 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.392304845 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.392304845 + 12 x = 10.392304845 + 12 Combine like terms: 10.392304845 + 12 = 22.392304845 x = 22.392304845 Simplifying x = 22.392304845

Subproblem 2

x + -12 = -10.392304845 Simplifying x + -12 = -10.392304845 Reorder the terms: -12 + x = -10.392304845 Solving -12 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.392304845 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.392304845 + 12 x = -10.392304845 + 12 Combine like terms: -10.392304845 + 12 = 1.607695155 x = 1.607695155 Simplifying x = 1.607695155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.392304845, 1.607695155}

See similar equations:

| 4(w+7)=3w-9 | | 3x+6-x=5+x+4 | | a^2-14a-16=0 | | 5b+7-4=4b+12b-3 | | 5/7x+3=-2/7x+6 | | 7x+3=4x+1 | | -4(y-8)=6-3y | | 6k*6=38k | | 7(6+3x)=105 | | 4x+5=5x-2x | | 9j*7=651 | | -110+14c=70+8c | | 1/3m+2/3m=-5 | | 47*h=282 | | 5x^(2/3)-44x^(1/3)-9=0 | | 7y+y=7y-2 | | 6g*4=244 | | -7x+2=0 | | 7/9=x/35 | | -5/16=x-7/8 | | 37*f=296 | | 1/2(2x-1)=7 | | 23=y-7 | | r+4.4=-9.5 | | y=-5x^2-8x+4 | | 91*c=63c | | 1/2(2x+1)=7 | | 4(3+y)=3(5+y) | | -2p(3p-2)= | | 9(m+2)=-7(m+7) | | 87*a=783 | | 3x+(17-9x)-(16-10)=30-23x |

Equations solver categories