4x^2-23x-4=0

Simple and best practice solution for 4x^2-23x-4=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^2-23x-4=0 equation:


Simplifying
4x2 + -23x + -4 = 0

Reorder the terms:
-4 + -23x + 4x2 = 0

Solving
-4 + -23x + 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'.
-1 + -5.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -5.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5.75x + x2 = 0 + 1
-5.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5.75x + x2 = 1

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = 1 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = 1 + 8.265625

Combine like terms: 1 + 8.265625 = 9.265625
8.265625 + -5.75x + x2 = 9.265625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 9.265625

Calculate the square root of the right side: 3.043948915

Break this problem into two subproblems by setting 
(x + -2.875) equal to 3.043948915 and -3.043948915.

Subproblem 1

x + -2.875 = 3.043948915 Simplifying x + -2.875 = 3.043948915 Reorder the terms: -2.875 + x = 3.043948915 Solving -2.875 + x = 3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.043948915 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.043948915 + 2.875 x = 3.043948915 + 2.875 Combine like terms: 3.043948915 + 2.875 = 5.918948915 x = 5.918948915 Simplifying x = 5.918948915

Subproblem 2

x + -2.875 = -3.043948915 Simplifying x + -2.875 = -3.043948915 Reorder the terms: -2.875 + x = -3.043948915 Solving -2.875 + x = -3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.043948915 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.043948915 + 2.875 x = -3.043948915 + 2.875 Combine like terms: -3.043948915 + 2.875 = -0.168948915 x = -0.168948915 Simplifying x = -0.168948915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.918948915, -0.168948915}

See similar equations:

| 2a-3=11f-24 | | x/-2-8=-7 | | 3(4g+1)-1g=8-(3g+2) | | {-1/3,4} | | 3(x)-2(x)=24 | | -2x-6=3(x-4) | | y^2-14y+43=0 | | 5+log^2(-5*x)=9 | | -4.9t^2+13t+1=0 | | 34-bf=10 | | 5+log^3(-5*x)=9 | | lx+9l=9 | | 14m=20 | | -22=-11(x+4) | | -a-5/2a=35/4 | | 34-be=10 | | 2x-1/3=8/4 | | -0.5n+n=1.25 | | -11(x+4)=-22 | | 3x+2y+8z=38 | | 68=5e+8 | | 8x+9.72=4x+17 | | 23=-7k-6k | | 4(12-8)+16= | | -10(s+3)=-61 | | 3x+2y+3z=38 | | -3x+16=5x-8 | | 23=7k-6k | | -4+14=13x-2-12x | | 68=5+8 | | 6(x-3)=7x-2(x+1) | | 8x-14=x-7 |

Equations solver categories