u^2-20u=30

Simple and best practice solution for u^2-20u=30 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 u^2-20u=30 equation:


Simplifying
u2 + -20u = 30

Reorder the terms:
-20u + u2 = 30

Solving
-20u + u2 = 30

Solving for variable 'u'.

Reorder the terms:
-30 + -20u + u2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -20u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -20u + 30 + u2 = 0 + 30

Reorder the terms:
-30 + 30 + -20u + u2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -20u + u2 = 0 + 30
-20u + u2 = 0 + 30

Combine like terms: 0 + 30 = 30
-20u + u2 = 30

The u term is -20u.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20u + 100 + u2 = 30 + 100

Reorder the terms:
100 + -20u + u2 = 30 + 100

Combine like terms: 30 + 100 = 130
100 + -20u + u2 = 130

Factor a perfect square on the left side:
(u + -10)(u + -10) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(u + -10) equal to 11.401754251 and -11.401754251.

Subproblem 1

u + -10 = 11.401754251 Simplifying u + -10 = 11.401754251 Reorder the terms: -10 + u = 11.401754251 Solving -10 + u = 11.401754251 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + u = 11.401754251 + 10 Combine like terms: -10 + 10 = 0 0 + u = 11.401754251 + 10 u = 11.401754251 + 10 Combine like terms: 11.401754251 + 10 = 21.401754251 u = 21.401754251 Simplifying u = 21.401754251

Subproblem 2

u + -10 = -11.401754251 Simplifying u + -10 = -11.401754251 Reorder the terms: -10 + u = -11.401754251 Solving -10 + u = -11.401754251 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + u = -11.401754251 + 10 Combine like terms: -10 + 10 = 0 0 + u = -11.401754251 + 10 u = -11.401754251 + 10 Combine like terms: -11.401754251 + 10 = -1.401754251 u = -1.401754251 Simplifying u = -1.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. u = {21.401754251, -1.401754251}

See similar equations:

| r^2+10r=1 | | v^2-16v-29=0 | | 3(y-6)=-6 | | 2Y+12=180 | | j^2-4j-49=0 | | 2y+12=360 | | m^2-14m=19 | | b/17-4b/17=15/17 | | k^2-26k=-29 | | 2y+12=8x+13 | | 2y+12=8x+13 | | r^2+26r+47=0 | | 38-18+6k=44 | | 2x/8-5/8+x/2-1/2=13x/4+3/4 | | 5/7x-6=7 | | x/3-x/4=2 | | 1+4x=-3x-76 | | b-9+7b=12 | | 23=4x+5-2x | | -4x-4=-39+3x | | 4.3=7.3-0.6x | | Y/4=15 | | 8+6x=x-7 | | -5x+4=-x-32 | | 9m^2+3m^4= | | (2x-6)(5x+2)=0 | | -4x+5=5x+104 | | 4+3x-2x=4 | | sqrtx=2 | | 7(x+5)=4(3x-5) | | 2x+4+5x=-38 | | -14=6x-4x+10 |

Equations solver categories