6x^2+30x-38=0

Simple and best practice solution for 6x^2+30x-38=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 6x^2+30x-38=0 equation: 


Simplifying
6x2 + 30x + -38 = 0

Reorder the terms:
-38 + 30x + 6x2 = 0

Solving
-38 + 30x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 15x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-19 + 15x + 3x2 = 0

Solving
-19 + 15x + 3x2 = 0

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

Divide each side by '3'.
-6.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 5x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 5x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + 6.333333333
5x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
5x + x2 = 6.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 6.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 6.333333333 + 6.25

Combine like terms: 6.333333333 + 6.25 = 12.583333333
6.25 + 5x + x2 = 12.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 12.583333333

Calculate the square root of the right side: 3.547299442

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.547299442 and -3.547299442.


Subproblem 1
x + 2.5 = 3.547299442

Simplifying
x + 2.5 = 3.547299442

Reorder the terms:
2.5 + x = 3.547299442

Solving
2.5 + x = 3.547299442

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.547299442 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.547299442 + -2.5
x = 3.547299442 + -2.5

Combine like terms: 3.547299442 + -2.5 = 1.047299442
x = 1.047299442

Simplifying
x = 1.047299442


Subproblem 2
x + 2.5 = -3.547299442

Simplifying
x + 2.5 = -3.547299442

Reorder the terms:
2.5 + x = -3.547299442

Solving
2.5 + x = -3.547299442

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.547299442 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.547299442 + -2.5
x = -3.547299442 + -2.5

Combine like terms: -3.547299442 + -2.5 = -6.047299442
x = -6.047299442

Simplifying
x = -6.047299442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.047299442, -6.047299442}
Solution
x = {1.047299442, -6.047299442}

See similar equations:

| 5p^2+12=-23p | | 2.18=[(4x+1)*.12]+.10x | | -4(z+4)+11=6z+35 | | t^2-18t+60.75= | | 5(7x+3)=15 | | -(7-4b)=16b+17 | | V^3-v^2-16v=-32 | | 4x+2+5x-5=180 | | 2x-9+6x=12x+1+x | | x^7-4=-2 | | 3x+22+140= | | 3a+-5a=2a+4 | | 8x+65=11(x+4) | | 21n^2+107n+105=-7-5n | | 7(x+1)2(6+5x)=7 | | t^2-22t+90.75= | | 100+2x=360 | | 2a-5a=2a+4 | | -7m+3m=17-53 | | 7(x+1)-2(6+5x)=7 | | 0.4x-0.2(60+x)=0.2(40) | | 4/7-(-3/8)= | | -3(0+7)+5*0=-21 | | 4/7-(-3/8) | | 7x+7-12+10x=7 | | 8+4(b-4)=-8+7b | | (-2x^4)+7=2x-3 | | 8x+65=11+x+4 | | a/4-a-2/3 | | 195/x=13 | | (2x+3y+1)dx+(2x+3y-5)dy=0 | | -m-8=12.4 |

Equations solver categories