(5x)(2x+5)=180

Simple and best practice solution for (5x)(2x+5)=180 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)(2x+5)=180 equation: 


Simplifying
(5x)(2x + 5) = 180

Remove parenthesis around (5x)
5x(2x + 5) = 180

Reorder the terms:
5x(5 + 2x) = 180
(5 * 5x + 2x * 5x) = 180
(25x + 10x2) = 180

Solving
25x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 25x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 25x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 5x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-36 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-36 + 5x + 2x2 = 0

Solving
-36 + 5x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-18 + 2.5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 2.5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 2.5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2.5x + x2 = 0 + 18
2.5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
2.5x + x2 = 18

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 18 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 18 + 1.5625

Combine like terms: 18 + 1.5625 = 19.5625
1.5625 + 2.5x + x2 = 19.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.422951503 and -4.422951503.


Subproblem 1
x + 1.25 = 4.422951503

Simplifying
x + 1.25 = 4.422951503

Reorder the terms:
1.25 + x = 4.422951503

Solving
1.25 + x = 4.422951503

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 4.422951503 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 4.422951503 + -1.25
x = 4.422951503 + -1.25

Combine like terms: 4.422951503 + -1.25 = 3.172951503
x = 3.172951503

Simplifying
x = 3.172951503


Subproblem 2
x + 1.25 = -4.422951503

Simplifying
x + 1.25 = -4.422951503

Reorder the terms:
1.25 + x = -4.422951503

Solving
1.25 + x = -4.422951503

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -4.422951503 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -4.422951503 + -1.25
x = -4.422951503 + -1.25

Combine like terms: -4.422951503 + -1.25 = -5.672951503
x = -5.672951503

Simplifying
x = -5.672951503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.172951503, -5.672951503}
Solution
x = {3.172951503, -5.672951503}

See similar equations:

| -2(5s-5)-10=-3(8s+0)-5 | | x^2+6x-182=0 | | 3.6=3(1.1y+1.8) | | x^2+6x-172=0 | | BC=9.5x+25.5 | | 5+2(n+2)=5n | | 0=3x^3-11x^2+4x | | 5a=-2(13-9a) | | -x^2+6x-172=0 | | 2-(x+7)=0 | | AB=15X-2 | | ln(x+11)=ln(x+6)+ln(x+3) | | 2x-y=18 | | -54x=78 | | 7x+2+x=1+5x+16 | | 8+n=11 | | -20.7=27.2+m | | -16t^2+160t-256=0 | | -16t^2+128t-256=0 | | 6x^2+6x-72=03 | | 12=a(a+1) | | 5x+45=2x+8 | | 5(x+3)+4(x-2)=-4 | | 11.37-3.459= | | x^2-6=y | | 6x+2=-3x+8 | | ln(x+12)+ln(x-5)=2lnx | | 4+2(z-2)=-4z+5 | | 3x-2z-8=0 | | x^2+19x= | | x+16x+64=0 | | -3a+4+4a=9-28 |

Equations solver categories