4x^2-9x-22=0

Simple and best practice solution for 4x^2-9x-22=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^2-9x-22=0 equation:


Simplifying
4x2 + -9x + -22 = 0

Reorder the terms:
-22 + -9x + 4x2 = 0

Solving
-22 + -9x + 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'.
-5.5 + -2.25x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -2.25x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -2.25x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -2.25x + x2 = 0 + 5.5
-2.25x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-2.25x + x2 = 5.5

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 5.5 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 5.5 + 1.265625

Combine like terms: 5.5 + 1.265625 = 6.765625
1.265625 + -2.25x + x2 = 6.765625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 6.765625

Calculate the square root of the right side: 2.601081506

Break this problem into two subproblems by setting 
(x + -1.125) equal to 2.601081506 and -2.601081506.

Subproblem 1

x + -1.125 = 2.601081506 Simplifying x + -1.125 = 2.601081506 Reorder the terms: -1.125 + x = 2.601081506 Solving -1.125 + x = 2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.601081506 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.601081506 + 1.125 x = 2.601081506 + 1.125 Combine like terms: 2.601081506 + 1.125 = 3.726081506 x = 3.726081506 Simplifying x = 3.726081506

Subproblem 2

x + -1.125 = -2.601081506 Simplifying x + -1.125 = -2.601081506 Reorder the terms: -1.125 + x = -2.601081506 Solving -1.125 + x = -2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.601081506 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.601081506 + 1.125 x = -2.601081506 + 1.125 Combine like terms: -2.601081506 + 1.125 = -1.476081506 x = -1.476081506 Simplifying x = -1.476081506

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.726081506, -1.476081506}

See similar equations:

| (5w+2)(8w+5)= | | 0=-32+16t^2-16t | | 8x+12y= | | 5x-7=40x+7 | | 44-12x=-8(x-7) | | 7x+7=5x+1 | | 2x-y=-18 | | 35x^3+21x+14^4/7x | | x/x-6-4=6/x-6 | | -3x^2-4x+224=0 | | 5z-11-2z+5=0 | | x/8-3=-5 | | X^2+3x-255=3x | | 4.5d=7.65 | | 2/5k-2(1/10k+3)=-k+24 | | 4x^2-6x+4=0 | | 3x+2(x-8)=x | | 3/5x+5/(x+1) | | 2(3m+4m)-9=45 | | 2(x+8)=4x+2 | | 8/4+(3x6) | | 4(1/2)p+(1/2)=7(1/4) | | -8(z-4)=-7z-5 | | 7x+8=8x | | 5z=-9 | | 9(w-5)-(-4w-1)=12w | | 4(m+2)-2=26 | | x^2+2x-112=0 | | x+5=-4x+71 | | ln(x-2)-ln(x+1)=ln(3) | | 5x+3(4x+2)= | | -6-(5-6p)= |

Equations solver categories