5x^2+75x+225=0

Simple and best practice solution for 5x^2+75x+225=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 5x^2+75x+225=0 equation: 


Simplifying
5x2 + 75x + 225 = 0

Reorder the terms:
225 + 75x + 5x2 = 0

Solving
225 + 75x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(45 + 15x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(45 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
45 + 15x + x2 = 0

Solving
45 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 15x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + 15x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 15x + x2 = 0 + -45
15x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
15x + x2 = -45

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -45 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -45 + 56.25

Combine like terms: -45 + 56.25 = 11.25
56.25 + 15x + x2 = 11.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 7.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 7.5 = 3.354101966

Simplifying
x + 7.5 = 3.354101966

Reorder the terms:
7.5 + x = 3.354101966

Solving
7.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 3.354101966 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 3.354101966 + -7.5
x = 3.354101966 + -7.5

Combine like terms: 3.354101966 + -7.5 = -4.145898034
x = -4.145898034

Simplifying
x = -4.145898034


Subproblem 2
x + 7.5 = -3.354101966

Simplifying
x + 7.5 = -3.354101966

Reorder the terms:
7.5 + x = -3.354101966

Solving
7.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -3.354101966 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -3.354101966 + -7.5
x = -3.354101966 + -7.5

Combine like terms: -3.354101966 + -7.5 = -10.854101966
x = -10.854101966

Simplifying
x = -10.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.145898034, -10.854101966}
Solution
x = {-4.145898034, -10.854101966}

See similar equations:

| 6=-8(3-w)-3w | | 7y=3ax+by | | 1/4+1/(x+2)=x | | 7y=3 | | w/8+2.2=-10.6 | | 3+5z-2=9z+1-3z | | 8x-8=20-6x | | z^4+2z^2-3=0 | | -21x^3-13x^2-2x=0 | | x/16=-7 | | -4=3x-17/2 | | 2(3x-5)=35-3(x+5) | | a+a+a/2+a/4+1=100 | | (x/2)/2+2x+(2x/2)+1=100 | | (x/2)/2+2x+1=100 | | (x/2)/2+2x+1 | | (x/2)/2+x+x+1=100 | | (x/2)/2+x+1=100 | | 3x+y=370 | | -6m-8=28 | | x+(x/2)/2+1=100 | | 9-3x-5-10x=7 | | 2.3q-2.5-2.1q=-0.8q-5.6 | | 8(x/(x-3)) | | 3+i/6+3i | | .2x^2+3x-20=0 | | 6+3i/3+i | | -2a+8+6a=5a-3a | | 4-1/2q=33-a | | 4(-1-2q)=3(12-q) | | -x^2-10x+75=0 | | 8n-2=17n-9 |

Equations solver categories