2(r^2-15r+40)=0

Simple and best practice solution for 2(r^2-15r+40)=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 2(r^2-15r+40)=0 equation: 


Simplifying
2(r2 + -15r + 40) = 0

Reorder the terms:
2(40 + -15r + r2) = 0
(40 * 2 + -15r * 2 + r2 * 2) = 0
(80 + -30r + 2r2) = 0

Solving
80 + -30r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -15r + r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -15r + r2)' equal to zero and attempt to solve:

Simplifying
40 + -15r + r2 = 0

Solving
40 + -15r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -15r + -40 + r2 = 0 + -40

Reorder the terms:
40 + -40 + -15r + r2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -15r + r2 = 0 + -40
-15r + r2 = 0 + -40

Combine like terms: 0 + -40 = -40
-15r + r2 = -40

The r term is -15r.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15r + 56.25 + r2 = -40 + 56.25

Reorder the terms:
56.25 + -15r + r2 = -40 + 56.25

Combine like terms: -40 + 56.25 = 16.25
56.25 + -15r + r2 = 16.25

Factor a perfect square on the left side:
(r + -7.5)(r + -7.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(r + -7.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
r + -7.5 = 4.031128874

Simplifying
r + -7.5 = 4.031128874

Reorder the terms:
-7.5 + r = 4.031128874

Solving
-7.5 + r = 4.031128874

Solving for variable 'r'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + r = 4.031128874 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + r = 4.031128874 + 7.5
r = 4.031128874 + 7.5

Combine like terms: 4.031128874 + 7.5 = 11.531128874
r = 11.531128874

Simplifying
r = 11.531128874


Subproblem 2
r + -7.5 = -4.031128874

Simplifying
r + -7.5 = -4.031128874

Reorder the terms:
-7.5 + r = -4.031128874

Solving
-7.5 + r = -4.031128874

Solving for variable 'r'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + r = -4.031128874 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + r = -4.031128874 + 7.5
r = -4.031128874 + 7.5

Combine like terms: -4.031128874 + 7.5 = 3.468871126
r = 3.468871126

Simplifying
r = 3.468871126


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.531128874, 3.468871126}
Solution
r = {11.531128874, 3.468871126}

See similar equations:

| 4.3h=81.7 | | -3x-15=19 | | t/7+7=13 | | (x-3)(x^2+11x+18)=0 | | 1+20x-3500=0 | | -x^3+9=2x^2-6x | | 15/1+2e^-0.5n=7.5 | | -6r-4(r-1)=-(r+5) | | M-(-7/10)=-1/1/5 | | -5(x-2)+3=14 | | T-(-3/1/6)=7/2/3 | | -2x^2-11x+6=0 | | -7x+1-6=9 | | 12/40=32/6 | | 30w-98=30w+22 | | 3/4+6x=29/4-7x | | ((4x-3)/5)=7 | | -4(-4v-3)=-3(1-5v) | | 12x^2-54x-30=0 | | (0.15)(0.3)= | | 16/x=32/8 | | n+6+n+2n=94 | | 190/841= | | 10/t+5=0 | | (4x-3/5)=7 | | 90/4=17/x | | (4x-3)/5=7 | | 81=-y+3x | | 5y-2=9y+3 | | -2x^2-11x+8=0 | | 8/22=x/55 | | (2/3)(9x-12)-4(x-3)=20 |

Equations solver categories