y^2-90y+180=0

Simple and best practice solution for y^2-90y+180=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^2-90y+180=0 equation:


Simplifying
y2 + -90y + 180 = 0

Reorder the terms:
180 + -90y + y2 = 0

Solving
180 + -90y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + -90y + -180 + y2 = 0 + -180

Reorder the terms:
180 + -180 + -90y + y2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + -90y + y2 = 0 + -180
-90y + y2 = 0 + -180

Combine like terms: 0 + -180 = -180
-90y + y2 = -180

The y term is -90y.  Take half its coefficient (-45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
-90y + 2025 + y2 = -180 + 2025

Reorder the terms:
2025 + -90y + y2 = -180 + 2025

Combine like terms: -180 + 2025 = 1845
2025 + -90y + y2 = 1845

Factor a perfect square on the left side:
(y + -45)(y + -45) = 1845

Calculate the square root of the right side: 42.95346319

Break this problem into two subproblems by setting 
(y + -45) equal to 42.95346319 and -42.95346319.

Subproblem 1

y + -45 = 42.95346319 Simplifying y + -45 = 42.95346319 Reorder the terms: -45 + y = 42.95346319 Solving -45 + y = 42.95346319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + y = 42.95346319 + 45 Combine like terms: -45 + 45 = 0 0 + y = 42.95346319 + 45 y = 42.95346319 + 45 Combine like terms: 42.95346319 + 45 = 87.95346319 y = 87.95346319 Simplifying y = 87.95346319

Subproblem 2

y + -45 = -42.95346319 Simplifying y + -45 = -42.95346319 Reorder the terms: -45 + y = -42.95346319 Solving -45 + y = -42.95346319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + y = -42.95346319 + 45 Combine like terms: -45 + 45 = 0 0 + y = -42.95346319 + 45 y = -42.95346319 + 45 Combine like terms: -42.95346319 + 45 = 2.04653681 y = 2.04653681 Simplifying y = 2.04653681

Solution

The solution to the problem is based on the solutions from the subproblems. y = {87.95346319, 2.04653681}

See similar equations:

| y^2-22y+105=0 | | 2x+1=(x-2)t | | 2x+1=tx-2t | | 4x-18=2x-5(3x-8)-7 | | 4b-4=6 | | 6(3x-6)-2(x+1)-17= | | 3(7-7m)+9(3+4m)=93 | | 2cos^2x+3cos^2x=2 | | x^2+7+2x^2+4=86 | | q=0.5kl | | 5x^2-170x+1445=0 | | 45=6(a-8)+3(6-7a) | | 20x+50y=900 | | h-6=-8.4 | | x^2-34x+154=0 | | -2(5x)=5(x+7) | | 8x+5x-21=63-8x | | b+0.62b=2.48 | | 1/√(sec^2X-1) | | 55-3x-2x+1= | | 39.96+0.50x=c | | c=39.96+0.50x | | 500=x+3 | | tan(2x)=2sin(2x) | | 15=-3y-4x | | 4x=1/21 | | 4(-x+1)=-2(x+2) | | 3cos(2x+1)-2=0 | | x^3-6x^2+5x+4=0 | | 4x^2+12=6x | | 2y+y-2y=20 | | (10x-18)÷2/5 |

Equations solver categories