6x^2+13x-3=0

Simple and best practice solution for 6x^2+13x-3=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+13x-3=0 equation: 


Simplifying
6x2 + 13x + -3 = 0

Reorder the terms:
-3 + 13x + 6x2 = 0

Solving
-3 + 13x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.5 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.166666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.166666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.166666667x + x2 = 0 + 0.5
2.166666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.166666667x + x2 = 0.5

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 0.5 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 0.5 + 1.173611113

Combine like terms: 0.5 + 1.173611113 = 1.673611113
1.173611113 + 2.166666667x + x2 = 1.673611113

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 1.673611113

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.293681225 and -1.293681225.


Subproblem 1
x + 1.083333334 = 1.293681225

Simplifying
x + 1.083333334 = 1.293681225

Reorder the terms:
1.083333334 + x = 1.293681225

Solving
1.083333334 + x = 1.293681225

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 1.293681225 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 1.293681225 + -1.083333334
x = 1.293681225 + -1.083333334

Combine like terms: 1.293681225 + -1.083333334 = 0.210347891
x = 0.210347891

Simplifying
x = 0.210347891


Subproblem 2
x + 1.083333334 = -1.293681225

Simplifying
x + 1.083333334 = -1.293681225

Reorder the terms:
1.083333334 + x = -1.293681225

Solving
1.083333334 + x = -1.293681225

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -1.293681225 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -1.293681225 + -1.083333334
x = -1.293681225 + -1.083333334

Combine like terms: -1.293681225 + -1.083333334 = -2.377014559
x = -2.377014559

Simplifying
x = -2.377014559


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.210347891, -2.377014559}

See similar equations:

| (-16x^2+1)(x-5)= | | 1-x=7 | | x^3+x^2-56x+63=0 | | 115+s=249 | | 3q/3-6=-4 | | 13x^2+8x-5= | | 9-9x=36-16x | | W^2+15w=54 | | -6x^2+13x=3 | | 6x^2+13x=3 | | 9x-8=-9 | | 8y^2-10-3= | | -2m(3m-9)+(-4m)(-2m+3)=0 | | -16x^2+1= | | 10x^2-2x= | | -b(-b^3-1)+4b^4=0 | | 5v-5=-6(v-1) | | a+45+a*5=876 | | 10.2*[(2*3.7)+8]= | | 4-x(x-3)=0 | | 9.6+[(3.1*2)-2.3]+16= | | 6+2x=-4 | | x^2*y^2=4xy+3x | | (2x-5)*(x-1)=0 | | 5(x-1)+3(x-4)=-11 | | 10=3-g | | 4k-14+3k=22 | | 64x^2-22x= | | 4[6x-5(x-3)]=10x+24 | | 20x^2+9x+1= | | x^2-8x=-27 | | (3a+4)=7 |

Equations solver categories