7r^2+60r=32

Simple and best practice solution for 7r^2+60r=32 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 7r^2+60r=32 equation:


Simplifying
7r2 + 60r = 32

Reorder the terms:
60r + 7r2 = 32

Solving
60r + 7r2 = 32

Solving for variable 'r'.

Reorder the terms:
-32 + 60r + 7r2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 60r + 7r2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-4.571428571 + 8.571428571r + r2 = 0

Move the constant term to the right:

Add '4.571428571' to each side of the equation.
-4.571428571 + 8.571428571r + 4.571428571 + r2 = 0 + 4.571428571

Reorder the terms:
-4.571428571 + 4.571428571 + 8.571428571r + r2 = 0 + 4.571428571

Combine like terms: -4.571428571 + 4.571428571 = 0.000000000
0.000000000 + 8.571428571r + r2 = 0 + 4.571428571
8.571428571r + r2 = 0 + 4.571428571

Combine like terms: 0 + 4.571428571 = 4.571428571
8.571428571r + r2 = 4.571428571

The r term is 8.571428571r.  Take half its coefficient (4.285714286).
Square it (18.36734694) and add it to both sides.

Add '18.36734694' to each side of the equation.
8.571428571r + 18.36734694 + r2 = 4.571428571 + 18.36734694

Reorder the terms:
18.36734694 + 8.571428571r + r2 = 4.571428571 + 18.36734694

Combine like terms: 4.571428571 + 18.36734694 = 22.938775511
18.36734694 + 8.571428571r + r2 = 22.938775511

Factor a perfect square on the left side:
(r + 4.285714286)(r + 4.285714286) = 22.938775511

Calculate the square root of the right side: 4.789444176

Break this problem into two subproblems by setting 
(r + 4.285714286) equal to 4.789444176 and -4.789444176.

Subproblem 1

r + 4.285714286 = 4.789444176 Simplifying r + 4.285714286 = 4.789444176 Reorder the terms: 4.285714286 + r = 4.789444176 Solving 4.285714286 + r = 4.789444176 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + r = 4.789444176 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + r = 4.789444176 + -4.285714286 r = 4.789444176 + -4.285714286 Combine like terms: 4.789444176 + -4.285714286 = 0.50372989 r = 0.50372989 Simplifying r = 0.50372989

Subproblem 2

r + 4.285714286 = -4.789444176 Simplifying r + 4.285714286 = -4.789444176 Reorder the terms: 4.285714286 + r = -4.789444176 Solving 4.285714286 + r = -4.789444176 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + r = -4.789444176 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + r = -4.789444176 + -4.285714286 r = -4.789444176 + -4.285714286 Combine like terms: -4.789444176 + -4.285714286 = -9.075158462 r = -9.075158462 Simplifying r = -9.075158462

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.50372989, -9.075158462}

See similar equations:

| 5h-4(5+h)=-32 | | 5(0)+7(6)=8 | | 7x+6=9x-3 | | ln(x+7)+ln(x-4)=2*ln(x) | | 10(x-1)-7(x+1)=4 | | 5-(2x-1)=10-x | | ln(x+5)+ln(x-3)=2ln(x) | | x^2+x+130=0 | | (w+4)(w+14)-w(w-10)=216 | | t(t-2)+2(2t-t)=t*t+4 | | t(t-2)+2(2t-t)=t^2+4 | | 18x+54=180 | | (x-x^2)(2x^2+x-1)=5+2x-3x^2 | | 2x-3x-18=5x-18+2x | | 10x+34=180 | | ln(x)+ln(x)=0 | | -3x-8+7x=34+9x-2 | | 3a+5c-9a= | | 20a-12(a-3)=4 | | 4a^2+b^2+4ab=0 | | 7x+32=12-x | | 9x=4y-6 | | 31+41t-t=40 | | 5x^2-7x-1=4x^2-11x-4 | | 5(t-4)=9(7-3) | | (-10+-1x)(13+-1x)=0 | | 12z^6-12z=x | | .375+.375=3.8 | | (n-1)+n=5 | | 9(9-2)+15=33 | | 10g-4g=54 | | x+3=4x-3 |

Equations solver categories