4x^2+21x-22=0

Simple and best practice solution for 4x^2+21x-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+21x-22=0 equation: 


Simplifying
4x2 + 21x + -22 = 0

Reorder the terms:
-22 + 21x + 4x2 = 0

Solving
-22 + 21x + 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 + 5.25x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 5.25x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 5.25x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 5.25x + x2 = 0 + 5.5
5.25x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
5.25x + x2 = 5.5

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = 5.5 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = 5.5 + 6.890625

Combine like terms: 5.5 + 6.890625 = 12.390625
6.890625 + 5.25x + x2 = 12.390625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 12.390625

Calculate the square root of the right side: 3.52003196

Break this problem into two subproblems by setting 
(x + 2.625) equal to 3.52003196 and -3.52003196.


Subproblem 1
x + 2.625 = 3.52003196

Simplifying
x + 2.625 = 3.52003196

Reorder the terms:
2.625 + x = 3.52003196

Solving
2.625 + x = 3.52003196

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = 3.52003196 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = 3.52003196 + -2.625
x = 3.52003196 + -2.625

Combine like terms: 3.52003196 + -2.625 = 0.89503196
x = 0.89503196

Simplifying
x = 0.89503196


Subproblem 2
x + 2.625 = -3.52003196

Simplifying
x + 2.625 = -3.52003196

Reorder the terms:
2.625 + x = -3.52003196

Solving
2.625 + x = -3.52003196

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = -3.52003196 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = -3.52003196 + -2.625
x = -3.52003196 + -2.625

Combine like terms: -3.52003196 + -2.625 = -6.14503196
x = -6.14503196

Simplifying
x = -6.14503196


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.89503196, -6.14503196}

See similar equations:

| 7x+30=30 | | 9i=37 | | 4y^2-17y+15=0 | | p=b+4a+4c | | lr+60=16 | | p=b+4a | | 3h=34 | | 6g=22 | | 5f=31 | | x^4-7x^2+144=0 | | 5a-2+4a=2a+12 | | 3a-5-2a=2a-3 | | (10-x)-7=-(2x+4)-9 | | -7(t+5)=0 | | 4*7-4= | | x+8=-12 | | 14-7-6= | | 4x+9=21 | | 2x-17=-7 | | 7x^4-7x-20=0 | | 8*3-4= | | 7+8*5= | | x+10=-13 | | 6-x=2-(9-2x) | | 4t-27=-45+t | | 7(4h-1)=13 | | -27=9(y+1) | | 10+9x=100 | | 10+9x=127 | | -3x+8=38 | | r+4r=25 | | 7x-4=9x-6 |

Equations solver categories