2x^2+15x+9=0

Simple and best practice solution for 2x^2+15x+9=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 2x^2+15x+9=0 equation: 


Simplifying
2x2 + 15x + 9 = 0

Reorder the terms:
9 + 15x + 2x2 = 0

Solving
9 + 15x + 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'.
4.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 7.5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 7.5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 7.5x + x2 = 0 + -4.5
7.5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
7.5x + x2 = -4.5

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -4.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -4.5 + 14.0625

Combine like terms: -4.5 + 14.0625 = 9.5625
14.0625 + 7.5x + x2 = 9.5625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.092329219 and -3.092329219.


Subproblem 1
x + 3.75 = 3.092329219

Simplifying
x + 3.75 = 3.092329219

Reorder the terms:
3.75 + x = 3.092329219

Solving
3.75 + x = 3.092329219

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.092329219 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.092329219 + -3.75
x = 3.092329219 + -3.75

Combine like terms: 3.092329219 + -3.75 = -0.657670781
x = -0.657670781

Simplifying
x = -0.657670781


Subproblem 2
x + 3.75 = -3.092329219

Simplifying
x + 3.75 = -3.092329219

Reorder the terms:
3.75 + x = -3.092329219

Solving
3.75 + x = -3.092329219

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.092329219 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.092329219 + -3.75
x = -3.092329219 + -3.75

Combine like terms: -3.092329219 + -3.75 = -6.842329219
x = -6.842329219

Simplifying
x = -6.842329219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.657670781, -6.842329219}

See similar equations:

| 24x^6-21x^3-3=0 | | 2(1/16) | | -12=-4/9w | | 2t^2-9t+9=0 | | 4(q-4)-2=6 | | -6a-12=33 | | 5t+2(t+3)-4t=4(t+1)-(t-2) | | 10=c/-4c/6 | | 1/4^2 | | -2=3t-17 | | -7-8=8x+28x | | 9x+9=-1 | | x^3+4x^2+9x+6=0 | | (27+36x+18x^3)-(24+36x+36x^2+54x^3)=0 | | 2w/9=4 | | (w+l)2=36 | | -4-2x=14 | | -9v+36=0 | | 6/7u=42 | | acx+b=-d | | -2(-6x-2)=100 | | -5.2x+1.1=-7.1-1.1x | | -15=-3y-3 | | 10v^2+11v-8=0 | | 9(x+2)-8=3x+6(1+x) | | 10/7=2u | | 56=7/8w | | N+20=N+36 | | 4p-3=2(-3+p)+3(4p-5) | | 4x/4=6/5 | | -7.3w+6=-1.3 | | -6=8+-2x |

Equations solver categories