9x^2+24x-22=0

Simple and best practice solution for 9x^2+24x-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 9x^2+24x-22=0 equation:


Simplifying
9x2 + 24x + -22 = 0

Reorder the terms:
-22 + 24x + 9x2 = 0

Solving
-22 + 24x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-2.444444444 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '2.444444444' to each side of the equation.
-2.444444444 + 2.666666667x + 2.444444444 + x2 = 0 + 2.444444444

Reorder the terms:
-2.444444444 + 2.444444444 + 2.666666667x + x2 = 0 + 2.444444444

Combine like terms: -2.444444444 + 2.444444444 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 2.444444444
2.666666667x + x2 = 0 + 2.444444444

Combine like terms: 0 + 2.444444444 = 2.444444444
2.666666667x + x2 = 2.444444444

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 2.444444444 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 2.444444444 + 1.777777780

Combine like terms: 2.444444444 + 1.777777780 = 4.222222224
1.777777780 + 2.666666667x + x2 = 4.222222224

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 4.222222224

Calculate the square root of the right side: 2.054804668

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 2.054804668 and -2.054804668.

Subproblem 1

x + 1.333333334 = 2.054804668 Simplifying x + 1.333333334 = 2.054804668 Reorder the terms: 1.333333334 + x = 2.054804668 Solving 1.333333334 + x = 2.054804668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 2.054804668 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 2.054804668 + -1.333333334 x = 2.054804668 + -1.333333334 Combine like terms: 2.054804668 + -1.333333334 = 0.721471334 x = 0.721471334 Simplifying x = 0.721471334

Subproblem 2

x + 1.333333334 = -2.054804668 Simplifying x + 1.333333334 = -2.054804668 Reorder the terms: 1.333333334 + x = -2.054804668 Solving 1.333333334 + x = -2.054804668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -2.054804668 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -2.054804668 + -1.333333334 x = -2.054804668 + -1.333333334 Combine like terms: -2.054804668 + -1.333333334 = -3.388138002 x = -3.388138002 Simplifying x = -3.388138002

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.721471334, -3.388138002}

See similar equations:

| 3+2n=-3 | | y=x^2+kx+100 | | 5x+3=3(x-3) | | 5x+42=2x+18 | | 32+2x=8x-16 | | 7x-68=9x-96 | | -12.19-0.5x=5.3(x+3.5) | | 7(3x+2)=3(x+2)-17 | | ln(x+3)-4=ln(x-5) | | 5+2(3y-1)=2y-5 | | 100x-4x^2=20 | | 4x^2-25x+14=-4x+9 | | 4v-24=8v | | 7(c+2.1)=14c-0.7 | | 56(7)= | | 1.5(y-10)=0.4-y | | 3x+21=48+2x | | -8=x-2y | | 14=p-8 | | 1/4t+1/3t=7/12 | | 0.05+0.01x=6x | | 2(x+3)=6x-12 | | 5(2x+3x)-20=55 | | 100-4x=20 | | 6x+3y=16 | | 100-4x= | | t^2=33 | | 3x+9=21x | | x+(x-6)+15=39 | | (X-1)(x+9)=0 | | 11.2t+2=4.7t+44.90 | | 9-4d=3 |

Equations solver categories