7r^2=70r+75

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Solution for 7r^2=70r+75 equation:


Simplifying
7r2 = 70r + 75

Reorder the terms:
7r2 = 75 + 70r

Solving
7r2 = 75 + 70r

Solving for variable 'r'.

Reorder the terms:
-75 + -70r + 7r2 = 75 + 70r + -75 + -70r

Reorder the terms:
-75 + -70r + 7r2 = 75 + -75 + 70r + -70r

Combine like terms: 75 + -75 = 0
-75 + -70r + 7r2 = 0 + 70r + -70r
-75 + -70r + 7r2 = 70r + -70r

Combine like terms: 70r + -70r = 0
-75 + -70r + 7r2 = 0

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

Divide each side by '7'.
-10.71428571 + -10r + r2 = 0

Move the constant term to the right:

Add '10.71428571' to each side of the equation.
-10.71428571 + -10r + 10.71428571 + r2 = 0 + 10.71428571

Reorder the terms:
-10.71428571 + 10.71428571 + -10r + r2 = 0 + 10.71428571

Combine like terms: -10.71428571 + 10.71428571 = 0.00000000
0.00000000 + -10r + r2 = 0 + 10.71428571
-10r + r2 = 0 + 10.71428571

Combine like terms: 0 + 10.71428571 = 10.71428571
-10r + r2 = 10.71428571

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 = 10.71428571 + 25

Reorder the terms:
25 + -10r + r2 = 10.71428571 + 25

Combine like terms: 10.71428571 + 25 = 35.71428571
25 + -10r + r2 = 35.71428571

Factor a perfect square on the left side:
(r + -5)(r + -5) = 35.71428571

Calculate the square root of the right side: 5.976143046

Break this problem into two subproblems by setting 
(r + -5) equal to 5.976143046 and -5.976143046.

Subproblem 1

r + -5 = 5.976143046 Simplifying r + -5 = 5.976143046 Reorder the terms: -5 + r = 5.976143046 Solving -5 + r = 5.976143046 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 = 5.976143046 + 5 Combine like terms: -5 + 5 = 0 0 + r = 5.976143046 + 5 r = 5.976143046 + 5 Combine like terms: 5.976143046 + 5 = 10.976143046 r = 10.976143046 Simplifying r = 10.976143046

Subproblem 2

r + -5 = -5.976143046 Simplifying r + -5 = -5.976143046 Reorder the terms: -5 + r = -5.976143046 Solving -5 + r = -5.976143046 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 = -5.976143046 + 5 Combine like terms: -5 + 5 = 0 0 + r = -5.976143046 + 5 r = -5.976143046 + 5 Combine like terms: -5.976143046 + 5 = -0.976143046 r = -0.976143046 Simplifying r = -0.976143046

Solution

The solution to the problem is based on the solutions from the subproblems. r = {10.976143046, -0.976143046}

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