y^2+3y-12=10

Simple and best practice solution for y^2+3y-12=10 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 y^2+3y-12=10 equation: 


Simplifying
y2 + 3y + -12 = 10

Reorder the terms:
-12 + 3y + y2 = 10

Solving
-12 + 3y + y2 = 10

Solving for variable 'y'.

Reorder the terms:
-12 + -10 + 3y + y2 = 10 + -10

Combine like terms: -12 + -10 = -22
-22 + 3y + y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-22 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 3y + 22 + y2 = 0 + 22

Reorder the terms:
-22 + 22 + 3y + y2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 3y + y2 = 0 + 22
3y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
3y + y2 = 22

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 = 22 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + 3y + y2 = 24.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(y + 1.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
y + 1.5 = 4.924428901

Simplifying
y + 1.5 = 4.924428901

Reorder the terms:
1.5 + y = 4.924428901

Solving
1.5 + y = 4.924428901

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 = 4.924428901 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 4.924428901 + -1.5
y = 4.924428901 + -1.5

Combine like terms: 4.924428901 + -1.5 = 3.424428901
y = 3.424428901

Simplifying
y = 3.424428901


Subproblem 2
y + 1.5 = -4.924428901

Simplifying
y + 1.5 = -4.924428901

Reorder the terms:
1.5 + y = -4.924428901

Solving
1.5 + y = -4.924428901

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 = -4.924428901 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -4.924428901 + -1.5
y = -4.924428901 + -1.5

Combine like terms: -4.924428901 + -1.5 = -6.424428901
y = -6.424428901

Simplifying
y = -6.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.424428901, -6.424428901}

See similar equations:

| y/2+5=-1 | | 5x+2(x-2)=4x+2(2x-1) | | 5x+6(x+1)=x-(x-3) | | y+5=x | | 2x^2-4=196 | | 3x+4-2=180 | | x/5+12=7 | | 30x+30+20x=180 | | 4x+5-7x=-7 | | 5x+6x-9=180 | | x+2+8x-2=180 | | 2/3+2=5 | | y=1.9x | | x+139+132 | | -2a+21+7a=6a-8a | | (4x-2)(3x+1)=o | | 5(3x-1)-15x= | | (3m^2n^-1/n^3)^-3 | | 3x=2(5-2x) | | x/8+4=-3 | | 6(7x-8)=-6 | | .07x+.11=.21x-.03 | | 2x+6-5(x+1)=4x+7 | | 49m^2+399m+392=0 | | -2y=72 | | 9/(-3/7) | | -3y=96 | | 7x-21=.7 | | 13,482/214 | | -(1-8x)=-1.5+7.8x | | 2x+1-x=12 | | 6s-4s-2s= |

Equations solver categories