6x^2+4x-17=0

Simple and best practice solution for 6x^2+4x-17=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+4x-17=0 equation: 


Simplifying
6x2 + 4x + -17 = 0

Reorder the terms:
-17 + 4x + 6x2 = 0

Solving
-17 + 4x + 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'.
-2.833333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 0.6666666667x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 0.6666666667x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 2.833333333
0.6666666667x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
0.6666666667x + x2 = 2.833333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 2.833333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 2.833333333 + 0.1111111112

Combine like terms: 2.833333333 + 0.1111111112 = 2.9444444442
0.1111111112 + 0.6666666667x + x2 = 2.9444444442

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 2.9444444442

Calculate the square root of the right side: 1.715938357

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.715938357 and -1.715938357.


Subproblem 1
x + 0.3333333334 = 1.715938357

Simplifying
x + 0.3333333334 = 1.715938357

Reorder the terms:
0.3333333334 + x = 1.715938357

Solving
0.3333333334 + x = 1.715938357

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.715938357 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.715938357 + -0.3333333334
x = 1.715938357 + -0.3333333334

Combine like terms: 1.715938357 + -0.3333333334 = 1.3826050236
x = 1.3826050236

Simplifying
x = 1.3826050236


Subproblem 2
x + 0.3333333334 = -1.715938357

Simplifying
x + 0.3333333334 = -1.715938357

Reorder the terms:
0.3333333334 + x = -1.715938357

Solving
0.3333333334 + x = -1.715938357

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.715938357 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.715938357 + -0.3333333334
x = -1.715938357 + -0.3333333334

Combine like terms: -1.715938357 + -0.3333333334 = -2.0492716904
x = -2.0492716904

Simplifying
x = -2.0492716904


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3826050236, -2.0492716904}

See similar equations:

| -5x+8=-6 | | 27+3x-32+x=4x-80-x+185 | | (4x-2)+(6x-10)=180 | | 10x^4+16x^3+4x^2=0 | | -7n^2=-567 | | 35d+58=-12d+62 | | x^2-21x+98=0 | | x^2-2x-21=3 | | 19j-22=-7j+30 | | 7b^2-63=0 | | 25c+14=33c-11 | | 12y-12=7y-4 | | 2x+50=3x-13 | | x^2+4y+27y+7=180 | | 4t^2/16t | | 3x-15=2x+54 | | 2m+15=15 | | 12y=7y+8 | | 19+2m=15 | | 19+20=2m | | -6(1x+9)=-6 | | 2m+15=19 | | 5n^2-20n+6=0 | | 2x-16=56+x | | -7(3x-5)=161 | | 3(x-4)=2x-(6+x) | | 5n^2-20n+6=10 | | Ax+B(c)= | | 4/x-2+1/x+2=26/x2-4 | | x+4=-3x+24 | | 1/10x=7/8 | | 3(4x-3)=27 |

Equations solver categories