y^2+3y-9=0

Simple and best practice solution for y^2+3y-9=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 y^2+3y-9=0 equation:


Simplifying
y2 + 3y + -9 = 0

Reorder the terms:
-9 + 3y + y2 = 0

Solving
-9 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 3y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + 3y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3y + y2 = 0 + 9
3y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
3y + y2 = 9

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 = 9 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + 3y + y2 = 11.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + 1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

y + 1.5 = 3.354101966 Simplifying y + 1.5 = 3.354101966 Reorder the terms: 1.5 + y = 3.354101966 Solving 1.5 + y = 3.354101966 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 = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 3.354101966 + -1.5 y = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 y = 1.854101966 Simplifying y = 1.854101966

Subproblem 2

y + 1.5 = -3.354101966 Simplifying y + 1.5 = -3.354101966 Reorder the terms: 1.5 + y = -3.354101966 Solving 1.5 + y = -3.354101966 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 = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -3.354101966 + -1.5 y = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 y = -4.854101966 Simplifying y = -4.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.854101966, -4.854101966}

See similar equations:

| 14x-1=-3(1-2x)+12 | | 4n+1=12+5m | | 3(x-4)+5=-2*-2 | | 0=2x^2+20x-238 | | 5x-(4x+8)=-4 | | -1=4+5a | | xy+3x=25 | | x^2-7=72 | | x+6-8x+4=8(x-8)-2(4x-2) | | 8x+7=20+2x | | 0.25(5b+11)=9 | | -3x^4+12x^3-6x^2=0 | | 10(z+2)-4(z-3)=3(z-4)+2(2-4) | | 3x^2-6x=5 | | x-2+9=25 | | x-6=-17 | | x^2(x^2-36)-16(x^2-36)=0 | | 10+7x=24 | | 10(x-1)=24 | | 4x^2-8x-55=0 | | 3h-4=13 | | 5y^2+36-32= | | 6x+5x+3+8=3x+4+7x | | m(3-x)=7-y | | -35+7v=7(-3+3v) | | (x+4)=24 | | 2(4x+1)+4x=14 | | (-2a)(-3b)= | | x-4=9-x | | X+x-25+3(x-25)=275 | | 7(10-5x)=455 | | -60x^2-111x-45=0 |

Equations solver categories