4x^2-31x-46=0

Simple and best practice solution for 4x^2-31x-46=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^2-31x-46=0 equation:


Simplifying
4x2 + -31x + -46 = 0

Reorder the terms:
-46 + -31x + 4x2 = 0

Solving
-46 + -31x + 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'.
-11.5 + -7.75x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -7.75x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -7.75x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -7.75x + x2 = 0 + 11.5
-7.75x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-7.75x + x2 = 11.5

The x term is -7.75x.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75x + 15.015625 + x2 = 11.5 + 15.015625

Reorder the terms:
15.015625 + -7.75x + x2 = 11.5 + 15.015625

Combine like terms: 11.5 + 15.015625 = 26.515625
15.015625 + -7.75x + x2 = 26.515625

Factor a perfect square on the left side:
(x + -3.875)(x + -3.875) = 26.515625

Calculate the square root of the right side: 5.149332481

Break this problem into two subproblems by setting 
(x + -3.875) equal to 5.149332481 and -5.149332481.

Subproblem 1

x + -3.875 = 5.149332481 Simplifying x + -3.875 = 5.149332481 Reorder the terms: -3.875 + x = 5.149332481 Solving -3.875 + x = 5.149332481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 5.149332481 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 5.149332481 + 3.875 x = 5.149332481 + 3.875 Combine like terms: 5.149332481 + 3.875 = 9.024332481 x = 9.024332481 Simplifying x = 9.024332481

Subproblem 2

x + -3.875 = -5.149332481 Simplifying x + -3.875 = -5.149332481 Reorder the terms: -3.875 + x = -5.149332481 Solving -3.875 + x = -5.149332481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -5.149332481 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -5.149332481 + 3.875 x = -5.149332481 + 3.875 Combine like terms: -5.149332481 + 3.875 = -1.274332481 x = -1.274332481 Simplifying x = -1.274332481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.024332481, -1.274332481}

See similar equations:

| 7-4b=-1-3b | | 3(8p+6)=186 | | -6x^2+7x+5=0 | | 12x+21=-15 | | 180=2x+(y-40) | | 8b-5=9+7b | | 84=-7(x-5) | | 3(40+20)=(x-3)*60 | | 3(5*2)=36 | | 3(40+20)=60 | | 3(40+20)=x-3 | | x+x+4+3x+16=180 | | 3x+13=71-9x | | 91=7(2n+3) | | 6(-3k+4)-5=145 | | 5(-1.26666)+5y=9 | | 154-4x=6x+19 | | 7+9x=10x | | 52-3u=8 | | -174=6(-4r+3) | | a^2+11a=-1 | | 0.333333333x=18 | | -36-2=13-9x | | w(w+2)=168 | | -2x+y=-19 | | 7(1+7x)=350 | | 0.2x=6 | | 4g^2-3g-2=0 | | 0.25x=-12 | | -m^2+m-2=-2m^2 | | 2xz=4x+6yx | | 4c^2-15c-25=0 |

Equations solver categories