3x^2+12x-16=0

Simple and best practice solution for 3x^2+12x-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+12x-16=0 equation: 


Simplifying
3x2 + 12x + -16 = 0

Reorder the terms:
-16 + 12x + 3x2 = 0

Solving
-16 + 12x + 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 + 4x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 4x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 4x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + 5.333333333
4x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
4x + x2 = 5.333333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 5.333333333 + 4

Reorder the terms:
4 + 4x + x2 = 5.333333333 + 4

Combine like terms: 5.333333333 + 4 = 9.333333333
4 + 4x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + 2) equal to 3.055050463 and -3.055050463.


Subproblem 1
x + 2 = 3.055050463

Simplifying
x + 2 = 3.055050463

Reorder the terms:
2 + x = 3.055050463

Solving
2 + x = 3.055050463

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.055050463 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.055050463 + -2
x = 3.055050463 + -2

Combine like terms: 3.055050463 + -2 = 1.055050463
x = 1.055050463

Simplifying
x = 1.055050463


Subproblem 2
x + 2 = -3.055050463

Simplifying
x + 2 = -3.055050463

Reorder the terms:
2 + x = -3.055050463

Solving
2 + x = -3.055050463

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.055050463 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.055050463 + -2
x = -3.055050463 + -2

Combine like terms: -3.055050463 + -2 = -5.055050463
x = -5.055050463

Simplifying
x = -5.055050463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.055050463, -5.055050463}

See similar equations:

| 8=-16c | | 1y+8=3y+4 | | M(x)=20x-x^2 | | (2*2*2*2-3*5)q+13=(2*9-4*4)q+0 | | .5b*.667b=192 | | -(3x-6)=8 | | -138=-8x-10 | | 5y-18=24 | | -4.2=p+3.2 | | 1k+4k=3k+6 | | 2y+3z=3 | | a^4-2401=0 | | n^2-6n=7 | | x-42=0 | | (x+1)(3x-2)=2x+5 | | 6w=2w-8 | | a^2401=0 | | 4=4+6x | | -x-7=-10 | | (3*5)t+(21-12)=15+3*3 | | (H+4)=11 | | 6x(6x-10)=-25 | | 132232x+433375645=656534 | | X+26=8-5(x-2) | | 12x+8(-44/7)=20 | | -54=x-23 | | 35x+25=40x | | 180-154=x | | 9.7x+8.2=5.0x-7 | | -7y=-44 | | 1+3s=40 | | -8(x+2)=10 |

Equations solver categories