2y^2+6y-16=0

Simple and best practice solution for 2y^2+6y-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 2y^2+6y-16=0 equation: 


Simplifying
2y2 + 6y + -16 = 0

Reorder the terms:
-16 + 6y + 2y2 = 0

Solving
-16 + 6y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 3y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
-8 + 3y + y2 = 0

Solving
-8 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + 3y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3y + y2 = 0 + 8
3y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
3y + y2 = 8

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 8 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3y + y2 = 10.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(y + 1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
y + 1.5 = 3.201562119

Simplifying
y + 1.5 = 3.201562119

Reorder the terms:
1.5 + y = 3.201562119

Solving
1.5 + y = 3.201562119

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 3.201562119 + -1.5
y = 3.201562119 + -1.5

Combine like terms: 3.201562119 + -1.5 = 1.701562119
y = 1.701562119

Simplifying
y = 1.701562119


Subproblem 2
y + 1.5 = -3.201562119

Simplifying
y + 1.5 = -3.201562119

Reorder the terms:
1.5 + y = -3.201562119

Solving
1.5 + y = -3.201562119

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -3.201562119 + -1.5
y = -3.201562119 + -1.5

Combine like terms: -3.201562119 + -1.5 = -4.701562119
y = -4.701562119

Simplifying
y = -4.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.701562119, -4.701562119}
Solution
y = {1.701562119, -4.701562119}

See similar equations:

| 12n-35=n^2 | | -2.4k-8=0.64 | | f(3)=-3+3 | | 4x-3y=15 | | 2x^2+11x+9=0 | | -3x^2-18x+2=0 | | f=5+2x | | -2x^2-3x+4=0 | | 6x^2-9=15 | | x^2+1.4x=1.2 | | x^3+5x^2-73x-77=0 | | 6y-4=50 | | 4(8x-7)=-8x+6(5x-3) | | 4+4(x-2)=24 | | x-8(2x+3)=21 | | 4c+13=-6c+9 | | 6d+4d+2d-7=5d | | 12x-3y-25=0 | | 4-3x=6x-8 | | 3x-3=4x+2 | | 3x-2=7-5x | | 2(y+3)=18 | | -8+5x=8+6x | | 49=-0.095x^2+1.74x+60 | | 19=-d+14 | | -7w+2=3w-8 | | 7y-5=3y+9 | | 4x-7=-3x+2 | | 2x+7=4x-3 | | 4-3x=4-5x | | 9x+1=3x-4 | | 3x+6x-7x=0 |

Equations solver categories