32x^2-108x-81=0

Simple and best practice solution for 32x^2-108x-81=0 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 32x^2-108x-81=0 equation:


Simplifying
32x2 + -108x + -81 = 0

Reorder the terms:
-81 + -108x + 32x2 = 0

Solving
-81 + -108x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-2.53125 + -3.375x + x2 = 0

Move the constant term to the right:

Add '2.53125' to each side of the equation.
-2.53125 + -3.375x + 2.53125 + x2 = 0 + 2.53125

Reorder the terms:
-2.53125 + 2.53125 + -3.375x + x2 = 0 + 2.53125

Combine like terms: -2.53125 + 2.53125 = 0.00000
0.00000 + -3.375x + x2 = 0 + 2.53125
-3.375x + x2 = 0 + 2.53125

Combine like terms: 0 + 2.53125 = 2.53125
-3.375x + x2 = 2.53125

The x term is -3.375x.  Take half its coefficient (-1.6875).
Square it (2.84765625) and add it to both sides.

Add '2.84765625' to each side of the equation.
-3.375x + 2.84765625 + x2 = 2.53125 + 2.84765625

Reorder the terms:
2.84765625 + -3.375x + x2 = 2.53125 + 2.84765625

Combine like terms: 2.53125 + 2.84765625 = 5.37890625
2.84765625 + -3.375x + x2 = 5.37890625

Factor a perfect square on the left side:
(x + -1.6875)(x + -1.6875) = 5.37890625

Calculate the square root of the right side: 2.319246914

Break this problem into two subproblems by setting 
(x + -1.6875) equal to 2.319246914 and -2.319246914.

Subproblem 1

x + -1.6875 = 2.319246914 Simplifying x + -1.6875 = 2.319246914 Reorder the terms: -1.6875 + x = 2.319246914 Solving -1.6875 + x = 2.319246914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 2.319246914 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 2.319246914 + 1.6875 x = 2.319246914 + 1.6875 Combine like terms: 2.319246914 + 1.6875 = 4.006746914 x = 4.006746914 Simplifying x = 4.006746914

Subproblem 2

x + -1.6875 = -2.319246914 Simplifying x + -1.6875 = -2.319246914 Reorder the terms: -1.6875 + x = -2.319246914 Solving -1.6875 + x = -2.319246914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -2.319246914 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -2.319246914 + 1.6875 x = -2.319246914 + 1.6875 Combine like terms: -2.319246914 + 1.6875 = -0.631746914 x = -0.631746914 Simplifying x = -0.631746914

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.006746914, -0.631746914}

See similar equations:

| 4x-7=10+4x | | -2x-4=-5x-22 | | 2/5x-1=5/8x | | 18w-10-6w=60 | | r-12=24 | | P/15=135 | | 3/8x=15/1 | | D/2.1 | | -7z=98 | | -5x+3=-77+33x | | 4(8-x)-3y=-3 | | X^2+10=9x-4 | | 12/1×9/2 | | ba-d=c | | 2x(x+14)=5x+1 | | -15=b-13 | | 25+14t=25+14(8) | | 5+25-9= | | 2/9x=12/1 | | h=-8t^2+5t+13 | | 3056890000000-15000000000x=3000000000 | | 13-8n=5-4n | | 5x-0.5x^2-5.5=11 | | 0.003*7= | | 3(24)-5y=12 | | 2/3×-1/6 | | 3-(x-5)=10(x+6) | | 2x^2+21x=100 | | 3x-60=12 | | 35+s=91 | | -12m=0 | | E-12.5=48.6 |

Equations solver categories