x*x+(x+3)*(x+3)=41

Simple and best practice solution for x*x+(x+3)*(x+3)=41 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 x*x+(x+3)*(x+3)=41 equation: 


Simplifying
x * x + (x + 3)(x + 3) = 41

Multiply x * x
x2 + (x + 3)(x + 3) = 41

Reorder the terms:
x2 + (3 + x)(x + 3) = 41

Reorder the terms:
x2 + (3 + x)(3 + x) = 41

Multiply (3 + x) * (3 + x)
x2 + (3(3 + x) + x(3 + x)) = 41
x2 + ((3 * 3 + x * 3) + x(3 + x)) = 41
x2 + ((9 + 3x) + x(3 + x)) = 41
x2 + (9 + 3x + (3 * x + x * x)) = 41
x2 + (9 + 3x + (3x + x2)) = 41

Combine like terms: 3x + 3x = 6x
x2 + (9 + 6x + x2) = 41

Reorder the terms:
9 + 6x + x2 + x2 = 41

Combine like terms: x2 + x2 = 2x2
9 + 6x + 2x2 = 41

Solving
9 + 6x + 2x2 = 41

Solving for variable 'x'.

Reorder the terms:
9 + -41 + 6x + 2x2 = 41 + -41

Combine like terms: 9 + -41 = -32
-32 + 6x + 2x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-32 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 3x + x2 = 0

Solving
-16 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 3x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3x + x2 = 0 + 16
3x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
3x + x2 = 16

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 16 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3x + x2 = 18.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 1.5 = 4.272001873

Simplifying
x + 1.5 = 4.272001873

Reorder the terms:
1.5 + x = 4.272001873

Solving
1.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.272001873 + -1.5
x = 4.272001873 + -1.5

Combine like terms: 4.272001873 + -1.5 = 2.772001873
x = 2.772001873

Simplifying
x = 2.772001873


Subproblem 2
x + 1.5 = -4.272001873

Simplifying
x + 1.5 = -4.272001873

Reorder the terms:
1.5 + x = -4.272001873

Solving
1.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.272001873 + -1.5
x = -4.272001873 + -1.5

Combine like terms: -4.272001873 + -1.5 = -5.772001873
x = -5.772001873

Simplifying
x = -5.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.772001873, -5.772001873}
Solution
x = {2.772001873, -5.772001873}

See similar equations:

| -2x^2+4=-x^2+x-7 | | .78n-62=.56n-48 | | 6a+7+1a=-18 | | 19=-8r-3r | | x-49=27 | | 2(-x)=(-x)+9 | | 5+4lnx=3 | | 3x+6+3x=54 | | y^2+2xy+12=0 | | 9x-x+5=260 | | X(x+4)=106 | | x(x-7)(2x-10)=0 | | .67y-9=2y+3 | | 3x-13+2x+4=116 | | -66=5x-4(x+15) | | y=-3tanpix | | 1=-8r-3r | | 2x-5+3x=110 | | 1=-r-3r | | ln(2x-5)=ln(6x-4) | | 5+7m+9m=11 | | 3n-5=2n+20 | | x^2-10xy-24y^2= | | x+x+25.12=213.52 | | 96(389-16x^2+20x^3)=0 | | Logx=1.7 | | 7+7/7+7*7-7=50 | | -4+7(1-2w)=32 | | ln(2x-4)=ln(6x-4) | | -6(8x-1)+19=10(2x+3) | | 3m+5f=51 | | 35x+13(81-x)=2241 |

Equations solver categories