3x^2-14x-16=0

Simple and best practice solution for 3x^2-14x-16=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^2-14x-16=0 equation: 


Simplifying
3x2 + -14x + -16 = 0

Reorder the terms:
-16 + -14x + 3x2 = 0

Solving
-16 + -14x + 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'.
-5.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -4.666666667x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -4.666666667x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 5.333333333
-4.666666667x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-4.666666667x + x2 = 5.333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 5.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 5.333333333 + 5.444444448

Combine like terms: 5.333333333 + 5.444444448 = 10.777777781
5.444444448 + -4.666666667x + x2 = 10.777777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 10.777777781

Calculate the square root of the right side: 3.282952601

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.282952601 and -3.282952601.


Subproblem 1
x + -2.333333334 = 3.282952601

Simplifying
x + -2.333333334 = 3.282952601

Reorder the terms:
-2.333333334 + x = 3.282952601

Solving
-2.333333334 + x = 3.282952601

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.282952601 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.282952601 + 2.333333334
x = 3.282952601 + 2.333333334

Combine like terms: 3.282952601 + 2.333333334 = 5.616285935
x = 5.616285935

Simplifying
x = 5.616285935


Subproblem 2
x + -2.333333334 = -3.282952601

Simplifying
x + -2.333333334 = -3.282952601

Reorder the terms:
-2.333333334 + x = -3.282952601

Solving
-2.333333334 + x = -3.282952601

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.282952601 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.282952601 + 2.333333334
x = -3.282952601 + 2.333333334

Combine like terms: -3.282952601 + 2.333333334 = -0.949619267
x = -0.949619267

Simplifying
x = -0.949619267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.616285935, -0.949619267}

See similar equations:

| 4+5x=2+4x | | 17=-2(W-4) | | 7-x=22 | | 12.8=4Z+0.5 | | 8x+4+18x-6=180 | | 2T+5=-205 | | 5-3x=37 | | 231-3x=42x+21 | | 23n-16=76 | | 2(x-2)+7=3 | | R-15=3 | | 24x-3y=5.7 | | 7(K-8)=-7 | | y-3=20 | | 3x+2+=-(x+)+3 | | 8x+4=18x-6 | | 4x-1=1+x | | 8x+4=-6 | | 10(3x*2)=70 | | 2x^2-24x+144=80 | | S-f=s+nx | | -68+2x=75-9x | | 2M-13.9=12.4 | | X^2-5xy+6=0 | | 11+7x=23+4x | | 9x^2-x-1=-x | | 2x-21=x+7 | | 20x=16x-6 | | -2=3x/(5)+1 | | x^2-4x-2=-x^2-x-3 | | -x^2+7x+10=0 | | 12=2+z/(-6) |

Equations solver categories