y^2+5y=-3

Simple and best practice solution for y^2+5y=-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+5y=-3 equation:


Simplifying
y2 + 5y = -3

Reorder the terms:
5y + y2 = -3

Solving
5y + y2 = -3

Solving for variable 'y'.

Reorder the terms:
3 + 5y + y2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 5y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y + y2 = 0 + -3
5y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
5y + y2 = -3

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = -3 + 6.25

Reorder the terms:
6.25 + 5y + y2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5y + y2 = 3.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(y + 2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

y + 2.5 = 1.802775638 Simplifying y + 2.5 = 1.802775638 Reorder the terms: 2.5 + y = 1.802775638 Solving 2.5 + y = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 1.802775638 + -2.5 y = 1.802775638 + -2.5 Combine like terms: 1.802775638 + -2.5 = -0.697224362 y = -0.697224362 Simplifying y = -0.697224362

Subproblem 2

y + 2.5 = -1.802775638 Simplifying y + 2.5 = -1.802775638 Reorder the terms: 2.5 + y = -1.802775638 Solving 2.5 + y = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -1.802775638 + -2.5 y = -1.802775638 + -2.5 Combine like terms: -1.802775638 + -2.5 = -4.302775638 y = -4.302775638 Simplifying y = -4.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.697224362, -4.302775638}

See similar equations:

| 3y-wy+6-2w= | | -8(n+3)+25=-6n-5 | | (6i)(6i)= | | -88+5x=9x+28 | | 5*(x-7)+x=6*(x-8)+13 | | (f-5)(2f+9)=0 | | 1+5p=-1+6p+3-5 | | 156=-4(-7-8n) | | -106-6x=9x+89 | | 2z+3=-7-2i | | 135=-k+5(1-5k) | | 12+17c=40c | | 22=1-7r-7 | | -4k+(5k-6)=3k-39 | | 4-5v=19 | | -(1-5n)=2(n+1)-3 | | 9=-v+2+88v | | 46=18+2x | | y^4+y^4+y^4+y^4= | | 6r-5r=3(r-8)+6(-4+r) | | 10x+14=343 | | 2x+4y=-19 | | 29=-(1+6p)-3(-4p-4) | | x^2-4cosx=0 | | 9x-4=-1+8x | | -81+6x=-3x+54 | | x^2+5x-4=0 | | -12+2x=x-3 | | (x-4)(x-1)=(x+4)(x+3) | | -(7x-1)+7(x+5)=35 | | 12=(25-x)-19-2x | | -6b-b=-24 |

Equations solver categories