7r^2=70r-174

Simple and best practice solution for 7r^2=70r-174 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=70r-174 equation:


Simplifying
7r2 = 70r + -174

Reorder the terms:
7r2 = -174 + 70r

Solving
7r2 = -174 + 70r

Solving for variable 'r'.

Reorder the terms:
174 + -70r + 7r2 = -174 + 70r + 174 + -70r

Reorder the terms:
174 + -70r + 7r2 = -174 + 174 + 70r + -70r

Combine like terms: -174 + 174 = 0
174 + -70r + 7r2 = 0 + 70r + -70r
174 + -70r + 7r2 = 70r + -70r

Combine like terms: 70r + -70r = 0
174 + -70r + 7r2 = 0

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

Divide each side by '7'.
24.85714286 + -10r + r2 = 0

Move the constant term to the right:

Add '-24.85714286' to each side of the equation.
24.85714286 + -10r + -24.85714286 + r2 = 0 + -24.85714286

Reorder the terms:
24.85714286 + -24.85714286 + -10r + r2 = 0 + -24.85714286

Combine like terms: 24.85714286 + -24.85714286 = 0.00000000
0.00000000 + -10r + r2 = 0 + -24.85714286
-10r + r2 = 0 + -24.85714286

Combine like terms: 0 + -24.85714286 = -24.85714286
-10r + r2 = -24.85714286

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = -24.85714286 + 25

Reorder the terms:
25 + -10r + r2 = -24.85714286 + 25

Combine like terms: -24.85714286 + 25 = 0.14285714
25 + -10r + r2 = 0.14285714

Factor a perfect square on the left side:
(r + -5)(r + -5) = 0.14285714

Calculate the square root of the right side: 0.377964469

Break this problem into two subproblems by setting 
(r + -5) equal to 0.377964469 and -0.377964469.

Subproblem 1

r + -5 = 0.377964469 Simplifying r + -5 = 0.377964469 Reorder the terms: -5 + r = 0.377964469 Solving -5 + r = 0.377964469 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 0.377964469 + 5 Combine like terms: -5 + 5 = 0 0 + r = 0.377964469 + 5 r = 0.377964469 + 5 Combine like terms: 0.377964469 + 5 = 5.377964469 r = 5.377964469 Simplifying r = 5.377964469

Subproblem 2

r + -5 = -0.377964469 Simplifying r + -5 = -0.377964469 Reorder the terms: -5 + r = -0.377964469 Solving -5 + r = -0.377964469 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -0.377964469 + 5 Combine like terms: -5 + 5 = 0 0 + r = -0.377964469 + 5 r = -0.377964469 + 5 Combine like terms: -0.377964469 + 5 = 4.622035531 r = 4.622035531 Simplifying r = 4.622035531

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.377964469, 4.622035531}

See similar equations:

| .22x-.6=.12x+3-.8x | | 2e=4e-15 | | 6*x+5=45 | | b^2-18b+n= | | 2a+1=-3a | | x^2+6x+n= | | 6x+2=29+3x | | 1/6c-5=-2/3c+9 | | 5p+7=2p+13 | | -132-10x=9+20 | | m^2=56-m | | .3n=12 | | 6f-5=43 | | x^3+9y=10 | | x^3+9y=1 | | x^4+x^3+2x+2=0 | | -3g+12=-5g-10 | | x^3+9y=5 | | x^3+9y=3 | | 1/8*8 | | 1/2(6-y)+2x=4-x | | -m/3=-2 | | (2x)/(x+4)=(-3x)/(4x-3) | | (x+3)(x+3)=-4x | | 81/4*22/9 | | (x+3)2=-4x | | 2(x+5)=18x-12 | | -8+k/3=-5 | | H^2-3h=40 | | 3a+4=3*8+1 | | 8p=-7 | | 5r+4(r+3)=66 |

Equations solver categories