x(2x+9)+5=0

Simple and best practice solution for x(2x+9)+5=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 x(2x+9)+5=0 equation: 


Simplifying
x(2x + 9) + 5 = 0

Reorder the terms:
x(9 + 2x) + 5 = 0
(9 * x + 2x * x) + 5 = 0
(9x + 2x2) + 5 = 0

Reorder the terms:
5 + 9x + 2x2 = 0

Solving
5 + 9x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
2.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4.5x + x2 = 0 + -2.5
4.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
4.5x + x2 = -2.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -2.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -2.5 + 5.0625

Combine like terms: -2.5 + 5.0625 = 2.5625
5.0625 + 4.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + 2.25 = 1.600781059

Simplifying
x + 2.25 = 1.600781059

Reorder the terms:
2.25 + x = 1.600781059

Solving
2.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 1.600781059 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 1.600781059 + -2.25
x = 1.600781059 + -2.25

Combine like terms: 1.600781059 + -2.25 = -0.649218941
x = -0.649218941

Simplifying
x = -0.649218941


Subproblem 2
x + 2.25 = -1.600781059

Simplifying
x + 2.25 = -1.600781059

Reorder the terms:
2.25 + x = -1.600781059

Solving
2.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -1.600781059 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -1.600781059 + -2.25
x = -1.600781059 + -2.25

Combine like terms: -1.600781059 + -2.25 = -3.850781059
x = -3.850781059

Simplifying
x = -3.850781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.649218941, -3.850781059}

See similar equations:

| 18+23=t-42 | | (9lnx)-1/2lny | | -y^2+8y-5=0 | | 1/2(2y-6)-1=-(4-y) | | (2x+6)=50 | | K=45 | | (4x+4)=(6x-6) | | 2(x-2)/3 | | 8x=10+x(3) | | 4m-4m-8=-2m+12 | | 9u^2-6=0 | | -7(p-894)=-210 | | -7m^2-9m=0 | | -3w-45=-8(w+5) | | 6+6(7-a)= | | 9v^2-v-5=0 | | 21(n+21)=336 | | 4(3c-1)-1=8c+3 | | 5+(-6)=27 | | -2j^2+2=0 | | 4+y=-2x | | 9b-1=42 | | 2u^2+9u+2=0 | | x^2+18x=32 | | 29-17=2(x-7) | | 76=4(n-77) | | -0.5x*32x^2+80x+0=96 | | -7d^2+7d+8=0 | | 5-t/7-t=2/t-7 | | -3-8x+4x^2=0 | | 4z^2-6=0 | | Z+4=-3 |

Equations solver categories