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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 = 28125 27225 + 330r + r2 = 28125 Factor a perfect square on the left side: (r + 165)(r + 165) = 28125 Calculate the square root of the right side: 167.705098312 Break this problem into two subproblems by setting (r + 165) equal to 167.705098312 and -167.705098312.Subproblem 1
r + 165 = 167.705098312 Simplifying r + 165 = 167.705098312 Reorder the terms: 165 + r = 167.705098312 Solving 165 + r = 167.705098312 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 = 167.705098312 + -165 Combine like terms: 165 + -165 = 0 0 + r = 167.705098312 + -165 r = 167.705098312 + -165 Combine like terms: 167.705098312 + -165 = 2.705098312 r = 2.705098312 Simplifying r = 2.705098312Subproblem 2
r + 165 = -167.705098312 Simplifying r + 165 = -167.705098312 Reorder the terms: 165 + r = -167.705098312 Solving 165 + r = -167.705098312 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 = -167.705098312 + -165 Combine like terms: 165 + -165 = 0 0 + r = -167.705098312 + -165 r = -167.705098312 + -165 Combine like terms: -167.705098312 + -165 = -332.705098312 r = -332.705098312 Simplifying r = -332.705098312Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.705098312, -332.705098312}
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