3X^2+17X-67=0

Simple and best practice solution for 3X^2+17X-67=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 3X^2+17X-67=0 equation: 


Simplifying
3X2 + 17X + -67 = 0

Reorder the terms:
-67 + 17X + 3X2 = 0

Solving
-67 + 17X + 3X2 = 0

Solving for variable 'X'.

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

Divide each side by '3'.
-22.33333333 + 5.666666667X + X2 = 0

Move the constant term to the right:

Add '22.33333333' to each side of the equation.
-22.33333333 + 5.666666667X + 22.33333333 + X2 = 0 + 22.33333333

Reorder the terms:
-22.33333333 + 22.33333333 + 5.666666667X + X2 = 0 + 22.33333333

Combine like terms: -22.33333333 + 22.33333333 = 0.00000000
0.00000000 + 5.666666667X + X2 = 0 + 22.33333333
5.666666667X + X2 = 0 + 22.33333333

Combine like terms: 0 + 22.33333333 = 22.33333333
5.666666667X + X2 = 22.33333333

The X term is 5.666666667X.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667X + 8.027777782 + X2 = 22.33333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667X + X2 = 22.33333333 + 8.027777782

Combine like terms: 22.33333333 + 8.027777782 = 30.361111112
8.027777782 + 5.666666667X + X2 = 30.361111112

Factor a perfect square on the left side:
(X + 2.833333334)(X + 2.833333334) = 30.361111112

Calculate the square root of the right side: 5.510091752

Break this problem into two subproblems by setting 
(X + 2.833333334) equal to 5.510091752 and -5.510091752.


Subproblem 1
X + 2.833333334 = 5.510091752

Simplifying
X + 2.833333334 = 5.510091752

Reorder the terms:
2.833333334 + X = 5.510091752

Solving
2.833333334 + X = 5.510091752

Solving for variable 'X'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + X = 5.510091752 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + X = 5.510091752 + -2.833333334
X = 5.510091752 + -2.833333334

Combine like terms: 5.510091752 + -2.833333334 = 2.676758418
X = 2.676758418

Simplifying
X = 2.676758418


Subproblem 2
X + 2.833333334 = -5.510091752

Simplifying
X + 2.833333334 = -5.510091752

Reorder the terms:
2.833333334 + X = -5.510091752

Solving
2.833333334 + X = -5.510091752

Solving for variable 'X'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + X = -5.510091752 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + X = -5.510091752 + -2.833333334
X = -5.510091752 + -2.833333334

Combine like terms: -5.510091752 + -2.833333334 = -8.343425086
X = -8.343425086

Simplifying
X = -8.343425086


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.676758418, -8.343425086}

See similar equations:

| 6x+y=-10 | | x/5=2 | | =100+50*2-4 | | 9x+10y=5 | | (x^2+5)(x^2-5)=56 | | 7y+3=3y-21 | | 5x+4x-3x+2= | | 30+x-x^2=0 | | -5x+8y=42 | | -46+t=19 | | 3x+2=x-7 | | 168-5x=6x+14 | | -10=x+9 | | -7.34-2.7x=-4.4x-4.79 | | 4w+9=-7 | | -3-(5-3p)= | | -30x+24=-12x+81 | | 3(2x-5)-6(3-4x)= | | x^2+24+144=4 | | 12x^2+11x-36= | | 15h+52b=x | | 8y-7+7y+8+6y+11=180 | | 2x+x=18688 | | 2x=18668 | | 2x+123=18668 | | 2p-15-13p=150-11 | | 10z=-8 | | 2n-1+2n+1+7=180 | | -6.3(3y+6)-2.7(2y-4)= | | 8x^2+48x-56=0 | | 5t-5/10=70 | | 2n-1+2n+1=180 |

Equations solver categories