y^2+7y-2=0

Simple and best practice solution for y^2+7y-2=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+7y-2=0 equation: 


Simplifying
y2 + 7y + -2 = 0

Reorder the terms:
-2 + 7y + y2 = 0

Solving
-2 + 7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 7y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 7y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7y + y2 = 0 + 2
7y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
7y + y2 = 2

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 = 2 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + 7y + y2 = 14.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 3.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
y + 3.5 = 3.774917218

Simplifying
y + 3.5 = 3.774917218

Reorder the terms:
3.5 + y = 3.774917218

Solving
3.5 + y = 3.774917218

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 = 3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 3.774917218 + -3.5
y = 3.774917218 + -3.5

Combine like terms: 3.774917218 + -3.5 = 0.274917218
y = 0.274917218

Simplifying
y = 0.274917218


Subproblem 2
y + 3.5 = -3.774917218

Simplifying
y + 3.5 = -3.774917218

Reorder the terms:
3.5 + y = -3.774917218

Solving
3.5 + y = -3.774917218

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 = -3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -3.774917218 + -3.5
y = -3.774917218 + -3.5

Combine like terms: -3.774917218 + -3.5 = -7.274917218
y = -7.274917218

Simplifying
y = -7.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.274917218, -7.274917218}

See similar equations:

| 0=-x^2+6x+16 | | 2x+9=-5x+79 | | -9k+4+7=22 | | 6(x+3)-6=20 | | 197-15-(1.5w)=176 | | 49+a=-38 | | -7x-10=-130+3x | | -3x+2=-7x+30 | | (3x+3)=(5x-3) | | 30-18=2x-6 | | -3x+9=-7x+30 | | 20x-2y=-30 | | -5-x=-6x+50 | | 4x+2=4x+40 | | 5(x)+y=2 | | 68+M=-29 | | 4(3x-2)=7(x+1) | | -3a+20+9a=4a-8a | | 0=14x^2+29x-15 | | (6m+3)-(4m-1)= | | 2/3n-36=22 | | 2x-7=-5+3x | | 0.1x-0.6x-9=1 | | 7log^3x=28 | | -6h+2h=24 | | 7-19x-5-2x=5 | | 1x+1x=5 | | y-(-4)=-3/4(x-16) | | 0=-2x^3-10x^2-12x | | 3z+12= | | S-4=2s+13 | | -2a+10+9a=6a-4a |

Equations solver categories