y^2=2y+5*3y-8

Simple and best practice solution for y^2=2y+5*3y-8 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=2y+5*3y-8 equation: 


Simplifying
y2 = 2y + 5 * 3y + -8

Multiply 5 * 3
y2 = 2y + 15y + -8

Reorder the terms:
y2 = -8 + 2y + 15y

Combine like terms: 2y + 15y = 17y
y2 = -8 + 17y

Solving
y2 = -8 + 17y

Solving for variable 'y'.

Reorder the terms:
8 + -17y + y2 = -8 + 17y + 8 + -17y

Reorder the terms:
8 + -17y + y2 = -8 + 8 + 17y + -17y

Combine like terms: -8 + 8 = 0
8 + -17y + y2 = 0 + 17y + -17y
8 + -17y + y2 = 17y + -17y

Combine like terms: 17y + -17y = 0
8 + -17y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -17y + -8 + y2 = 0 + -8

Reorder the terms:
8 + -8 + -17y + y2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -17y + y2 = 0 + -8
-17y + y2 = 0 + -8

Combine like terms: 0 + -8 = -8
-17y + y2 = -8

The y term is -17y.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17y + 72.25 + y2 = -8 + 72.25

Reorder the terms:
72.25 + -17y + y2 = -8 + 72.25

Combine like terms: -8 + 72.25 = 64.25
72.25 + -17y + y2 = 64.25

Factor a perfect square on the left side:
(y + -8.5)(y + -8.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(y + -8.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
y + -8.5 = 8.015609771

Simplifying
y + -8.5 = 8.015609771

Reorder the terms:
-8.5 + y = 8.015609771

Solving
-8.5 + y = 8.015609771

Solving for variable 'y'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + y = 8.015609771 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = 8.015609771 + 8.5
y = 8.015609771 + 8.5

Combine like terms: 8.015609771 + 8.5 = 16.515609771
y = 16.515609771

Simplifying
y = 16.515609771


Subproblem 2
y + -8.5 = -8.015609771

Simplifying
y + -8.5 = -8.015609771

Reorder the terms:
-8.5 + y = -8.015609771

Solving
-8.5 + y = -8.015609771

Solving for variable 'y'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + y = -8.015609771 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = -8.015609771 + 8.5
y = -8.015609771 + 8.5

Combine like terms: -8.015609771 + 8.5 = 0.484390229
y = 0.484390229

Simplifying
y = 0.484390229


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.515609771, 0.484390229}

See similar equations:

| 50*1= | | y=x^3-13x^2+35x+1 | | x^2-5=-5 | | 2log(x)=log(2)+log(4x+10) | | U=-8x-13y-5x+7y | | y=ln(ln*7x) | | U=166+41(6) | | 2*x=5*y+5 | | 2x-4x-12=8 | | X+X=580 | | 4/5m=-12 | | 3z^2+19z+20=0 | | Cos^2x-sinx=0 | | Log(3x+7)=3 | | -26=-2+4x | | 5(y-2)+(y-3)= | | 7x-16=32 | | 15m+5=0 | | -3m-7=-31-m | | -3x^2+8x= | | x=y*2 | | 2m-3n=17 | | 2x(x-y)-y(2y-2x)= | | 7x+16=32 | | 6x^3y-3xy^2= | | 4a(a+b)= | | X-69+69-69=69 | | 2/9×-1/3=-1 | | X+8+3-18=33 | | x^4-18x+22x= | | X-14+19=21 | | 2(10x+10)=0 |

Equations solver categories