y^2+5=578y

Simple and best practice solution for y^2+5=578y 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+5=578y equation:


Simplifying
y2 + 5 = 578y

Reorder the terms:
5 + y2 = 578y

Solving
5 + y2 = 578y

Solving for variable 'y'.

Reorder the terms:
5 + -578y + y2 = 578y + -578y

Combine like terms: 578y + -578y = 0
5 + -578y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -578y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -578y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -578y + y2 = 0 + -5
-578y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-578y + y2 = -5

The y term is -578y.  Take half its coefficient (-289).
Square it (83521) and add it to both sides.

Add '83521' to each side of the equation.
-578y + 83521 + y2 = -5 + 83521

Reorder the terms:
83521 + -578y + y2 = -5 + 83521

Combine like terms: -5 + 83521 = 83516
83521 + -578y + y2 = 83516

Factor a perfect square on the left side:
(y + -289)(y + -289) = 83516

Calculate the square root of the right side: 288.991349351

Break this problem into two subproblems by setting 
(y + -289) equal to 288.991349351 and -288.991349351.

Subproblem 1

y + -289 = 288.991349351 Simplifying y + -289 = 288.991349351 Reorder the terms: -289 + y = 288.991349351 Solving -289 + y = 288.991349351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '289' to each side of the equation. -289 + 289 + y = 288.991349351 + 289 Combine like terms: -289 + 289 = 0 0 + y = 288.991349351 + 289 y = 288.991349351 + 289 Combine like terms: 288.991349351 + 289 = 577.991349351 y = 577.991349351 Simplifying y = 577.991349351

Subproblem 2

y + -289 = -288.991349351 Simplifying y + -289 = -288.991349351 Reorder the terms: -289 + y = -288.991349351 Solving -289 + y = -288.991349351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '289' to each side of the equation. -289 + 289 + y = -288.991349351 + 289 Combine like terms: -289 + 289 = 0 0 + y = -288.991349351 + 289 y = -288.991349351 + 289 Combine like terms: -288.991349351 + 289 = 0.008650649 y = 0.008650649 Simplifying y = 0.008650649

Solution

The solution to the problem is based on the solutions from the subproblems. y = {577.991349351, 0.008650649}

See similar equations:

| 7x+9=4x-49 | | 6x+16=2x+88 | | x^7+x^5-6x^3=0 | | 2x+144=8x+60 | | 6x+56=2x+116 | | 15x+7=52 | | 8x-5x= | | 10x^2-89=9 | | 2x+18=8x+66 | | =4r^2+15r-4 | | 4[2(3)+3(5)]= | | 2N+5=29 | | 5x-12=6x-1 | | N-17=23 | | y-7.5x=0 | | 12(x-8)=4(5-2x)+3(7-3x) | | 4x+3y=8 | | 197-2x=43x+22 | | 33*45=b*15 | | X+5+15+2x=35 | | 6*18=4*x | | 3y+4x=8 | | 3*20=4*n | | 2x^3-10x^2+4x-20= | | 5x-2=2x-11 | | 7y=2x | | 4.2*.5=6.3*.3 | | 11*25=13*22 | | 5*28=7*20 | | x-5.6=-17.9 | | 19g=g+16 | | N(x)-m=p |

Equations solver categories