r^2+30r=37

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Solution for r^2+30r=37 equation:


Simplifying
r2 + 30r = 37

Reorder the terms:
30r + r2 = 37

Solving
30r + r2 = 37

Solving for variable 'r'.

Reorder the terms:
-37 + 30r + r2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 30r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 30r + 37 + r2 = 0 + 37

Reorder the terms:
-37 + 37 + 30r + r2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 30r + r2 = 0 + 37
30r + r2 = 0 + 37

Combine like terms: 0 + 37 = 37
30r + r2 = 37

The r term is 30r.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30r + 225 + r2 = 37 + 225

Reorder the terms:
225 + 30r + r2 = 37 + 225

Combine like terms: 37 + 225 = 262
225 + 30r + r2 = 262

Factor a perfect square on the left side:
(r + 15)(r + 15) = 262

Calculate the square root of the right side: 16.186414056

Break this problem into two subproblems by setting 
(r + 15) equal to 16.186414056 and -16.186414056.

Subproblem 1

r + 15 = 16.186414056 Simplifying r + 15 = 16.186414056 Reorder the terms: 15 + r = 16.186414056 Solving 15 + r = 16.186414056 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + r = 16.186414056 + -15 Combine like terms: 15 + -15 = 0 0 + r = 16.186414056 + -15 r = 16.186414056 + -15 Combine like terms: 16.186414056 + -15 = 1.186414056 r = 1.186414056 Simplifying r = 1.186414056

Subproblem 2

r + 15 = -16.186414056 Simplifying r + 15 = -16.186414056 Reorder the terms: 15 + r = -16.186414056 Solving 15 + r = -16.186414056 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + r = -16.186414056 + -15 Combine like terms: 15 + -15 = 0 0 + r = -16.186414056 + -15 r = -16.186414056 + -15 Combine like terms: -16.186414056 + -15 = -31.186414056 r = -31.186414056 Simplifying r = -31.186414056

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.186414056, -31.186414056}

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