y^2+9y=-3

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


Simplifying
y2 + 9y = -3

Reorder the terms:
9y + y2 = -3

Solving
9y + y2 = -3

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = -3 + 20.25

Reorder the terms:
20.25 + 9y + y2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9y + y2 = 17.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(y + 4.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

y + 4.5 = 4.153311931 Simplifying y + 4.5 = 4.153311931 Reorder the terms: 4.5 + y = 4.153311931 Solving 4.5 + y = 4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 4.153311931 + -4.5 y = 4.153311931 + -4.5 Combine like terms: 4.153311931 + -4.5 = -0.346688069 y = -0.346688069 Simplifying y = -0.346688069

Subproblem 2

y + 4.5 = -4.153311931 Simplifying y + 4.5 = -4.153311931 Reorder the terms: 4.5 + y = -4.153311931 Solving 4.5 + y = -4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -4.153311931 + -4.5 y = -4.153311931 + -4.5 Combine like terms: -4.153311931 + -4.5 = -8.653311931 y = -8.653311931 Simplifying y = -8.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.346688069, -8.653311931}

See similar equations:

| 387=3+8(8-8n) | | 7x-17=x+9 | | w+w+4w=12 | | -7(8v-5)=147 | | -102=-8(5-n)+2 | | 2(a+bi)-i(a-bi)=2+2i | | 4x^2-13x+10=-6x+7 | | .6t+.4(t-.3)=4.15 | | -119=3(1-7k)+4 | | 9(4v-2)=8(3v-9) | | 7x^2=38 | | 2p-8(8p+8)=246 | | (9x+7w)+(3x+8y)+(3y+5w)= | | 88=8(1-2m) | | 2-(2x-3)=1+(5x-1) | | 16x^2+58x-63=0 | | 8(p-4)=-96 | | 8(m-5)-7(m+2)=-54 | | 3p+4q-8(3p-8q+2r)= | | ln(3x+7)=0 | | -12z+4z+-19=5 | | 4x+3-2xy-5x-7+4yx= | | 2.6y-1=.22+2y | | -2(-3a+8)+6a=-100 | | 3x-5=5(x-9)+3 | | -8x+3=-4x-13 | | 35z^3+16z^2-12z=0 | | 3h-6=0 | | 15x+20y+9=0 | | 113=7(1+7r)+8 | | -3n+16+5n=34 | | 9(3x+8)=9(6x+4) |

Equations solver categories