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Simplifying 0.03r2 + -0.42r = 0.15 Reorder the terms: -0.42r + 0.03r2 = 0.15 Solving -0.42r + 0.03r2 = 0.15 Solving for variable 'r'. Reorder the terms: -0.15 + -0.42r + 0.03r2 = 0.15 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 -0.15 + -0.42r + 0.03r2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -5 + -14r + r2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -14r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + -14r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -14r + r2 = 0 + 5 -14r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 -14r + r2 = 5 The r term is -14r. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14r + 49 + r2 = 5 + 49 Reorder the terms: 49 + -14r + r2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + -14r + r2 = 54 Factor a perfect square on the left side: (r + -7)(r + -7) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (r + -7) equal to 7.348469228 and -7.348469228.Subproblem 1
r + -7 = 7.348469228 Simplifying r + -7 = 7.348469228 Reorder the terms: -7 + r = 7.348469228 Solving -7 + r = 7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = 7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + r = 7.348469228 + 7 r = 7.348469228 + 7 Combine like terms: 7.348469228 + 7 = 14.348469228 r = 14.348469228 Simplifying r = 14.348469228Subproblem 2
r + -7 = -7.348469228 Simplifying r + -7 = -7.348469228 Reorder the terms: -7 + r = -7.348469228 Solving -7 + r = -7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = -7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + r = -7.348469228 + 7 r = -7.348469228 + 7 Combine like terms: -7.348469228 + 7 = -0.348469228 r = -0.348469228 Simplifying r = -0.348469228Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.348469228, -0.348469228}
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