y^2+10y-21=0

Simple and best practice solution for y^2+10y-21=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+10y-21=0 equation: 


Simplifying
y2 + 10y + -21 = 0

Reorder the terms:
-21 + 10y + y2 = 0

Solving
-21 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 10y + 21 + y2 = 0 + 21

Reorder the terms:
-21 + 21 + 10y + y2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 10y + y2 = 0 + 21
10y + y2 = 0 + 21

Combine like terms: 0 + 21 = 21
10y + y2 = 21

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = 21 + 25

Reorder the terms:
25 + 10y + y2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + 10y + y2 = 46

Factor a perfect square on the left side:
(y + 5)(y + 5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(y + 5) equal to 6.782329983 and -6.782329983.


Subproblem 1
y + 5 = 6.782329983

Simplifying
y + 5 = 6.782329983

Reorder the terms:
5 + y = 6.782329983

Solving
5 + y = 6.782329983

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + y = 6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + y = 6.782329983 + -5
y = 6.782329983 + -5

Combine like terms: 6.782329983 + -5 = 1.782329983
y = 1.782329983

Simplifying
y = 1.782329983


Subproblem 2
y + 5 = -6.782329983

Simplifying
y + 5 = -6.782329983

Reorder the terms:
5 + y = -6.782329983

Solving
5 + y = -6.782329983

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + y = -6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + y = -6.782329983 + -5
y = -6.782329983 + -5

Combine like terms: -6.782329983 + -5 = -11.782329983
y = -11.782329983

Simplifying
y = -11.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.782329983, -11.782329983}

See similar equations:

| 3(x+3)-2=5x-2(-5+x) | | 7/x-4=-4x/x-1 | | 135-81*2/(17*2-5*5) | | 700=9x-(3.5x+60) | | 700=9x-3.5x+60 | | 35=x+2x+x | | -7(4x-9)+3=-28x+66 | | 3(1-m)= | | 2-(X/147)=0 | | 2x-9-5=0 | | 8Z/7=-z | | 3.5x-60=9x | | 2x=53+3 | | 9a+1=8a | | 3m+4m-5=25 | | 0.5x-0.1(4-3x)=0.6(x-4) | | x/8-1=-2 | | x/8-=-2 | | Abs(3u-3)=abs(3u-6) | | 10x+223=360 | | 2.0-(x/1.274)=0 | | 11x=x+20 | | 18x^2+2-(6(x^2-6)+5)= | | 10x+114=180 | | 2-(1.27/X)=0 | | 6X+35=-2X+11 | | 2-(127.40/X)=0 | | 40000-2.5=0 | | Y/55=5 | | -2(r-6)+10=8 | | m+8-2=13+5 | | 4r^2=-21+31r |

Equations solver categories