6x^2+45x=0-24

Simple and best practice solution for 6x^2+45x=0-24 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 6x^2+45x=0-24 equation: 


Simplifying
6x2 + 45x = 0 + -24

Reorder the terms:
45x + 6x2 = 0 + -24

Combine like terms: 0 + -24 = -24
45x + 6x2 = -24

Solving
45x + 6x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + 45x + 6x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 45x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 15x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + 15x + 2x2 = 0

Solving
8 + 15x + 2x2 = 0

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

Divide each side by '2'.
4 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 7.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 7.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7.5x + x2 = 0 + -4
7.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
7.5x + x2 = -4

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 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -4 + 14.0625

Combine like terms: -4 + 14.0625 = 10.0625
14.0625 + 7.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.172144385 and -3.172144385.


Subproblem 1
x + 3.75 = 3.172144385

Simplifying
x + 3.75 = 3.172144385

Reorder the terms:
3.75 + x = 3.172144385

Solving
3.75 + x = 3.172144385

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 = 3.172144385 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.172144385 + -3.75
x = 3.172144385 + -3.75

Combine like terms: 3.172144385 + -3.75 = -0.577855615
x = -0.577855615

Simplifying
x = -0.577855615


Subproblem 2
x + 3.75 = -3.172144385

Simplifying
x + 3.75 = -3.172144385

Reorder the terms:
3.75 + x = -3.172144385

Solving
3.75 + x = -3.172144385

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 = -3.172144385 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.172144385 + -3.75
x = -3.172144385 + -3.75

Combine like terms: -3.172144385 + -3.75 = -6.922144385
x = -6.922144385

Simplifying
x = -6.922144385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.577855615, -6.922144385}
Solution
x = {-0.577855615, -6.922144385}

See similar equations:

| 2sin(x)=0 | | 7p-1-2p-5= | | 8x^2+30x-7=0 | | 63+63w= | | 2sin=0 | | 3x+5(3x-3)=75 | | 2/3-1/6x=0.07 | | 2x=8x-3-4x | | -7x-4=-32 | | 8x^3-12x^2+20x= | | 95=p+29 | | 16x^2=1670 | | (-0.11)(-0.15)= | | 2sin^2x-6cosx+1=0 | | 0.03-0.02=0.07 | | 95=9+29 | | b^2-6b+11=10 | | 12+12y=12y+12 | | x=4-5x | | 6x^2-47x=8 | | 29=-12x | | 87=t+72 | | 3p^2+17p-28=0 | | 7x+2(4x-21)=108 | | 21+-2y=-29+3y | | n^2-20n+101=2 | | -12m+8=0 | | x+79+22=180 | | 798=436+x | | 79+22=x | | 40=-16t^2+40 | | 5x+2(4x+21)=107 |

Equations solver categories