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