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Simplifying r2 + -330r + 900 = 0 Reorder the terms: 900 + -330r + r2 = 0 Solving 900 + -330r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-900' to each side of the equation. 900 + -330r + -900 + r2 = 0 + -900 Reorder the terms: 900 + -900 + -330r + r2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + -330r + r2 = 0 + -900 -330r + r2 = 0 + -900 Combine like terms: 0 + -900 = -900 -330r + r2 = -900 The r term is -330r. Take half its coefficient (-165). Square it (27225) and add it to both sides. Add '27225' to each side of the equation. -330r + 27225 + r2 = -900 + 27225 Reorder the terms: 27225 + -330r + r2 = -900 + 27225 Combine like terms: -900 + 27225 = 26325 27225 + -330r + r2 = 26325 Factor a perfect square on the left side: (r + -165)(r + -165) = 26325 Calculate the square root of the right side: 162.249807396 Break this problem into two subproblems by setting (r + -165) equal to 162.249807396 and -162.249807396.Subproblem 1
r + -165 = 162.249807396 Simplifying r + -165 = 162.249807396 Reorder the terms: -165 + r = 162.249807396 Solving -165 + r = 162.249807396 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '165' to each side of the equation. -165 + 165 + r = 162.249807396 + 165 Combine like terms: -165 + 165 = 0 0 + r = 162.249807396 + 165 r = 162.249807396 + 165 Combine like terms: 162.249807396 + 165 = 327.249807396 r = 327.249807396 Simplifying r = 327.249807396Subproblem 2
r + -165 = -162.249807396 Simplifying r + -165 = -162.249807396 Reorder the terms: -165 + r = -162.249807396 Solving -165 + r = -162.249807396 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '165' to each side of the equation. -165 + 165 + r = -162.249807396 + 165 Combine like terms: -165 + 165 = 0 0 + r = -162.249807396 + 165 r = -162.249807396 + 165 Combine like terms: -162.249807396 + 165 = 2.750192604 r = 2.750192604 Simplifying r = 2.750192604Solution
The solution to the problem is based on the solutions from the subproblems. r = {327.249807396, 2.750192604}
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