4x^2-41x-82=0

Simple and best practice solution for 4x^2-41x-82=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 4x^2-41x-82=0 equation:


Simplifying
4x2 + -41x + -82 = 0

Reorder the terms:
-82 + -41x + 4x2 = 0

Solving
-82 + -41x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-20.5 + -10.25x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + -10.25x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + -10.25x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + -10.25x + x2 = 0 + 20.5
-10.25x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
-10.25x + x2 = 20.5

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = 20.5 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = 20.5 + 26.265625

Combine like terms: 20.5 + 26.265625 = 46.765625
26.265625 + -10.25x + x2 = 46.765625

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 46.765625

Calculate the square root of the right side: 6.838539683

Break this problem into two subproblems by setting 
(x + -5.125) equal to 6.838539683 and -6.838539683.

Subproblem 1

x + -5.125 = 6.838539683 Simplifying x + -5.125 = 6.838539683 Reorder the terms: -5.125 + x = 6.838539683 Solving -5.125 + x = 6.838539683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 6.838539683 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 6.838539683 + 5.125 x = 6.838539683 + 5.125 Combine like terms: 6.838539683 + 5.125 = 11.963539683 x = 11.963539683 Simplifying x = 11.963539683

Subproblem 2

x + -5.125 = -6.838539683 Simplifying x + -5.125 = -6.838539683 Reorder the terms: -5.125 + x = -6.838539683 Solving -5.125 + x = -6.838539683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -6.838539683 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -6.838539683 + 5.125 x = -6.838539683 + 5.125 Combine like terms: -6.838539683 + 5.125 = -1.713539683 x = -1.713539683 Simplifying x = -1.713539683

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.963539683, -1.713539683}

See similar equations:

| z^3+z^2+35z=0 | | .2n-(20)=-17 | | X-19+3x=5 | | 9x-14=6x+7 | | 9(-2)-10=3(-2)+2 | | 21a-11=10 | | 0=-2x^2+8x-6 | | -6f+13=2f-12 | | 9(3+7r)=33 | | X+5x+(5x-10)=180 | | 5x*6x=30 | | 3x=7x+-20 | | 3.7x=2.2x+12.0 | | 5(x+2)=34 | | .2n-20=-17 | | 1.495a-4.2(4.62+6.5a)=187.036 | | 19-6-k+4= | | 6x+12=-33 | | 22f+8(9-f)=128 | | 0.8(x+300)=0.85x-130 | | 4-3n+2n=n | | 7x=23.8 | | 3(2x-6)+6x=4x+6 | | -2(x+1)+9x=-9 | | 22f+8p=128 | | 3a^2-2=19 | | 3c+5c= | | 3(1+7b)+2=-142 | | m-4=17 | | 3(x-8)+8x=-2 | | 4(2x+6)=-31+15 | | 4x-7(4x-15)=-15 |

Equations solver categories