2x^2+22x+54=0

Simple and best practice solution for 2x^2+22x+54=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 2x^2+22x+54=0 equation: 


Simplifying
2x2 + 22x + 54 = 0

Reorder the terms:
54 + 22x + 2x2 = 0

Solving
54 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 11x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(27 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
27 + 11x + x2 = 0

Solving
27 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 11x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 11x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 11x + x2 = 0 + -27
11x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
11x + x2 = -27

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -27 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -27 + 30.25

Combine like terms: -27 + 30.25 = 3.25
30.25 + 11x + x2 = 3.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 5.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 5.5 = 1.802775638

Simplifying
x + 5.5 = 1.802775638

Reorder the terms:
5.5 + x = 1.802775638

Solving
5.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 1.802775638 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 1.802775638 + -5.5
x = 1.802775638 + -5.5

Combine like terms: 1.802775638 + -5.5 = -3.697224362
x = -3.697224362

Simplifying
x = -3.697224362


Subproblem 2
x + 5.5 = -1.802775638

Simplifying
x + 5.5 = -1.802775638

Reorder the terms:
5.5 + x = -1.802775638

Solving
5.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -1.802775638 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -1.802775638 + -5.5
x = -1.802775638 + -5.5

Combine like terms: -1.802775638 + -5.5 = -7.302775638
x = -7.302775638

Simplifying
x = -7.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.697224362, -7.302775638}
Solution
x = {-3.697224362, -7.302775638}

See similar equations:

| (7+3y)2= | | 6x=3(2x+5) | | 180k^2+300k+125=0 | | 6m-(31m-18)=12(m-1)+3m | | y=8-(1/2)x | | 160x^2-250=0 | | -3c^2+4c-4= | | h=25433(9.5)+28.465 | | 6x+8-4x=20 | | 4(k-2)-6=3k-(2k-3) | | m+m+18=31 | | 243g^2+54g+3=0 | | 61*ln(y)=13 | | 4/3p=9/8 | | 5(2x-6)=25 | | 2(p+9)= | | 4x-3y+z=4 | | 4x+3(2-3x)=40 | | 3x=5+2(3+1x) | | 3(x+3)-3=7(x+1)-4x | | x^3+2x^2+x= | | (x-1)(-6x+6)= | | 7x-5(x+1)+9=19 | | -16.49(4)+5.2= | | ln(5x-13)=4 | | y(2y-8)=0 | | 3(7Y)= | | 5.4(3+2x)-4.2=12 | | 5(x-1)+3(2x-1)=3 | | 4.17x+0.94=3.7x | | 1.7(-9.7x+6)-5= | | 0.1x+0.3= |

Equations solver categories