6x^2+13x-10=0

Simple and best practice solution for 6x^2+13x-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+13x-10=0 equation:


Simplifying
6x2 + 13x + -10 = 0

Reorder the terms:
-10 + 13x + 6x2 = 0

Solving
-10 + 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'.
-1.666666667 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2.166666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2.166666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + 1.666666667
2.166666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2.166666667x + x2 = 1.666666667

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 = 1.666666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 1.666666667 + 1.173611113

Combine like terms: 1.666666667 + 1.173611113 = 2.84027778
1.173611113 + 2.166666667x + x2 = 2.84027778

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 2.84027778

Calculate the square root of the right side: 1.685312369

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.685312369 and -1.685312369.

Subproblem 1

x + 1.083333334 = 1.685312369 Simplifying x + 1.083333334 = 1.685312369 Reorder the terms: 1.083333334 + x = 1.685312369 Solving 1.083333334 + x = 1.685312369 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 = 1.685312369 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 1.685312369 + -1.083333334 x = 1.685312369 + -1.083333334 Combine like terms: 1.685312369 + -1.083333334 = 0.601979035 x = 0.601979035 Simplifying x = 0.601979035

Subproblem 2

x + 1.083333334 = -1.685312369 Simplifying x + 1.083333334 = -1.685312369 Reorder the terms: 1.083333334 + x = -1.685312369 Solving 1.083333334 + x = -1.685312369 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 = -1.685312369 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -1.685312369 + -1.083333334 x = -1.685312369 + -1.083333334 Combine like terms: -1.685312369 + -1.083333334 = -2.768645703 x = -2.768645703 Simplifying x = -2.768645703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.601979035, -2.768645703}

See similar equations:

| 8q=-10q+36 | | 6u=28-u | | 6-2x=6x-10x+8 | | 12k+13=8k+33 | | 35=-7t | | 0.5(5+y)=0.25y | | -5t-14=2t | | 12-20=2t+2t | | -5t-14=21 | | 12-20=2t | | 45=-9(e+8) | | a=0 | | 3x-5y=30 | | x^2=x+1 | | 13+x=19 | | 7(5x-4)=5-(10-23X) | | x^2+6x=-9 | | 3x-16x=x | | 3x-16x= | | 9w+9=3w-15 | | 8.6=w-4.3 | | -8(3-s)=32 | | -3s=10 | | -7-2x+3x^2=0 | | 4(x+10)=2x+30 | | 9p=6p+21 | | 4h+6=2h-8 | | 9x^2+2x+9=0 | | 11x+5x= | | k+16=32 | | x^2-4x=0 | | 5c+15=2c-12 |

Equations solver categories