x^2+(x+3)(x+3)=15

Simple and best practice solution for x^2+(x+3)(x+3)=15 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^2+(x+3)(x+3)=15 equation: 


Simplifying
x2 + (x + 3)(x + 3) = 15

Reorder the terms:
x2 + (3 + x)(x + 3) = 15

Reorder the terms:
x2 + (3 + x)(3 + x) = 15

Multiply (3 + x) * (3 + x)
x2 + (3(3 + x) + x(3 + x)) = 15
x2 + ((3 * 3 + x * 3) + x(3 + x)) = 15
x2 + ((9 + 3x) + x(3 + x)) = 15
x2 + (9 + 3x + (3 * x + x * x)) = 15
x2 + (9 + 3x + (3x + x2)) = 15

Combine like terms: 3x + 3x = 6x
x2 + (9 + 6x + x2) = 15

Reorder the terms:
9 + 6x + x2 + x2 = 15

Combine like terms: x2 + x2 = 2x2
9 + 6x + 2x2 = 15

Solving
9 + 6x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
9 + -15 + 6x + 2x2 = 15 + -15

Combine like terms: 9 + -15 = -6
-6 + 6x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-6 + 6x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-3 + 3x + x2 = 0

Solving
-3 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 3 + 2.25

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

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3x + x2 = 5.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + 1.5 = 2.291287847

Simplifying
x + 1.5 = 2.291287847

Reorder the terms:
1.5 + x = 2.291287847

Solving
1.5 + x = 2.291287847

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 = 2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.291287847 + -1.5
x = 2.291287847 + -1.5

Combine like terms: 2.291287847 + -1.5 = 0.791287847
x = 0.791287847

Simplifying
x = 0.791287847


Subproblem 2
x + 1.5 = -2.291287847

Simplifying
x + 1.5 = -2.291287847

Reorder the terms:
1.5 + x = -2.291287847

Solving
1.5 + x = -2.291287847

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 = -2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.291287847 + -1.5
x = -2.291287847 + -1.5

Combine like terms: -2.291287847 + -1.5 = -3.791287847
x = -3.791287847

Simplifying
x = -3.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.791287847, -3.791287847}
Solution
x = {0.791287847, -3.791287847}

See similar equations:

| -6=2.3z | | Ln(x+4)+ln(x-4)=0 | | 31=-1.6n | | t.4=-13 | | Ln(x+4)ln(x-4)=0 | | 3v+7=-2.5 | | (x-1)(2x-5)=9 | | -d.7=-13 | | -84=d.3 | | a.16=9 | | x^2+4x^2+40x+100=625 | | x^2+4x^2+40x+100=25 | | c.4=16 | | 3(2m+4)=6(m+15) | | 0=x^2+5x+7 | | 3(2n+2)=8(6n+2)+5 | | 1/4*4(3)= | | 2n^2+36=-18n | | 2c-3c=45 | | 2c-c=45 | | 180=x+(2x+10)+25 | | -7+=49 | | (d+8)6= | | 4x^2-20x+53=0 | | 140=w(w+4) | | 2(5)+5(0)=15 | | 6/(3+2)=6/5 | | (4y-3)(3y^2+3y-8)= | | x.7-0.5=2.5 | | -16t^2+112t+288=0 | | -16t^2+112t+288=h | | 3k-7.5=16 |

Equations solver categories