6x^2+18x-10=0

Simple and best practice solution for 6x^2+18x-10=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+18x-10=0 equation: 


Simplifying
6x2 + 18x + -10 = 0

Reorder the terms:
-10 + 18x + 6x2 = 0

Solving
-10 + 18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 9x + 3x2 = 0

Solving
-5 + 9x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 3x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 3x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 3x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 3x + x2 = 0 + 1.666666667
3x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
3x + x2 = 1.666666667

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.666666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.666666667 + 2.25

Combine like terms: 1.666666667 + 2.25 = 3.916666667
2.25 + 3x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
x + 1.5 = 1.979057015

Simplifying
x + 1.5 = 1.979057015

Reorder the terms:
1.5 + x = 1.979057015

Solving
1.5 + x = 1.979057015

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.979057015 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.979057015 + -1.5
x = 1.979057015 + -1.5

Combine like terms: 1.979057015 + -1.5 = 0.479057015
x = 0.479057015

Simplifying
x = 0.479057015


Subproblem 2
x + 1.5 = -1.979057015

Simplifying
x + 1.5 = -1.979057015

Reorder the terms:
1.5 + x = -1.979057015

Solving
1.5 + x = -1.979057015

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.979057015 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.979057015 + -1.5
x = -1.979057015 + -1.5

Combine like terms: -1.979057015 + -1.5 = -3.479057015
x = -3.479057015

Simplifying
x = -3.479057015


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.479057015, -3.479057015}
Solution
x = {0.479057015, -3.479057015}

See similar equations:

| 1.8y+1.7=11.56 | | 0=-5t^2+12t-7.2 | | 3p-25=6 | | 2n+5=5n-5 | | 2x-3=13x-66 | | 8.3=4k-25 | | p+14=s | | -48=3k-3 | | 5x^2-11x+4= | | 30.76b=-73.8 | | 40=98-0.54t | | 40=98-0.54 | | 3(x-4)+5=3x+8 | | x^2-xy+y^2=13 | | 35=2+0.54t | | 35=2+0.54 | | -2,000,000-80,000x=4,200,000 | | 12X+12y=132 | | 12v=u | | 55=98-0.54t | | 17-c=-9 | | -6m+12=18 | | -2,000,000-80,000=-4,200,000 | | 18=v+u | | 775+n=977 | | 188+88x=14 | | p-6=s | | -2,000,000-80,000=-3,600,000 | | S=16p | | 10x-8=2x+2 | | Y=x^4-2x^3-8x+16 | | 3q-7p=-36 |

Equations solver categories