2x(2x+15)+x=180

Simple and best practice solution for 2x(2x+15)+x=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 2x(2x+15)+x=180 equation:


Simplifying
2x(2x + 15) + x = 180

Reorder the terms:
2x(15 + 2x) + x = 180
(15 * 2x + 2x * 2x) + x = 180
(30x + 4x2) + x = 180

Reorder the terms:
30x + x + 4x2 = 180

Combine like terms: 30x + x = 31x
31x + 4x2 = 180

Solving
31x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 31x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 31x + 4x2 = 0

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

Divide each side by '4'.
-45 + 7.75x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 7.75x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 7.75x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 7.75x + x2 = 0 + 45
7.75x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
7.75x + x2 = 45

The x term is 7.75x.  Take half its coefficient (3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
7.75x + 15.015625 + x2 = 45 + 15.015625

Reorder the terms:
15.015625 + 7.75x + x2 = 45 + 15.015625

Combine like terms: 45 + 15.015625 = 60.015625
15.015625 + 7.75x + x2 = 60.015625

Factor a perfect square on the left side:
(x + 3.875)(x + 3.875) = 60.015625

Calculate the square root of the right side: 7.746975216

Break this problem into two subproblems by setting 
(x + 3.875) equal to 7.746975216 and -7.746975216.

Subproblem 1

x + 3.875 = 7.746975216 Simplifying x + 3.875 = 7.746975216 Reorder the terms: 3.875 + x = 7.746975216 Solving 3.875 + x = 7.746975216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = 7.746975216 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = 7.746975216 + -3.875 x = 7.746975216 + -3.875 Combine like terms: 7.746975216 + -3.875 = 3.871975216 x = 3.871975216 Simplifying x = 3.871975216

Subproblem 2

x + 3.875 = -7.746975216 Simplifying x + 3.875 = -7.746975216 Reorder the terms: 3.875 + x = -7.746975216 Solving 3.875 + x = -7.746975216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = -7.746975216 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = -7.746975216 + -3.875 x = -7.746975216 + -3.875 Combine like terms: -7.746975216 + -3.875 = -11.621975216 x = -11.621975216 Simplifying x = -11.621975216

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.871975216, -11.621975216}

See similar equations:

| 15-10y=60 | | (9-x)=3x+4 | | x+17=482 | | 18+3x=36 | | 15x=75 | | 4(v+4)=3(v+3) | | 34x^2-16x+22=0 | | 4x^2+7=43 | | -3a-5+4a-6+2a=19 | | t^2-t=12 | | 4f-5=7 | | 3d+11=5 | | x+14+x=90 | | 2p+5=16 | | 1in=cm | | 27in=cm | | -82-7x=5x+1 | | 6x-10=-46 | | 8y-4x=10 | | x-8=29 | | x+(x-5)+(x+3)+(x+8)=360 | | (2x-7)*(2x-7)-125=(3x+2)*(3x+2) | | x-29=8 | | 6y=3x-6 | | (2x-7)2-125=(3x+2)2 | | x^2-4x+16=0 | | x+(x+8)+2x=180 | | y*5=10 | | 0.4x-5=0.25x+0.1x | | w-9=-14 | | 4xy-8=0 | | .3x=9 |

Equations solver categories