y^2+7y=-3

Simple and best practice solution for y^2+7y=-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+7y=-3 equation:


Simplifying
y2 + 7y = -3

Reorder the terms:
7y + y2 = -3

Solving
7y + y2 = -3

Solving for variable 'y'.

Reorder the terms:
3 + 7y + y2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 7y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7y + y2 = 0 + -3
7y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
7y + y2 = -3

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = -3 + 12.25

Reorder the terms:
12.25 + 7y + y2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7y + y2 = 9.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + 3.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

y + 3.5 = 3.041381265 Simplifying y + 3.5 = 3.041381265 Reorder the terms: 3.5 + y = 3.041381265 Solving 3.5 + y = 3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 3.041381265 + -3.5 y = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 y = -0.458618735 Simplifying y = -0.458618735

Subproblem 2

y + 3.5 = -3.041381265 Simplifying y + 3.5 = -3.041381265 Reorder the terms: 3.5 + y = -3.041381265 Solving 3.5 + y = -3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -3.041381265 + -3.5 y = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 y = -6.541381265 Simplifying y = -6.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.458618735, -6.541381265}

See similar equations:

| -1(-2x-4)-x-2=-7 | | -3n+10+n=18 | | -3(v+25)=11 | | 3=3(x-3)+1-2x | | 4n+21=2.50 | | -7n+24+9n=50 | | 2/3-1/2x-2=-1 | | d^2-8d-12=2 | | 3x-15=-12 | | 2x-25=-35 | | b^2-4b+1=6 | | 3(5x+y)-4(x-4y)= | | (n+5)*7=70 | | 4(3x+4)+5x+5=-115 | | 10+x/3=5 | | -3(5x+5)+2x+4=80 | | 6-x+12=10x-7 | | (n-3)*4=8 | | 2+2/6=5 | | 2(-2x+3)-2x+2=20 | | n^2+2n-5=0 | | 5(2x+6)-6(4x+6)= | | -0.5gt^2+vt+h=h | | 3/4x*15 | | y^2+x^2=121 | | 29.95-.10+300m=99.95 | | 1.33d^2+5=2 | | 135+somthing=180 | | 4x^2+9x+2-16=6x^2 | | 10p+5pd-2p+6pd= | | c(x)=x+50x-1030 | | 19x^3-38x^2= |

Equations solver categories