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Simplifying 25r2 + 4 = -21r Reorder the terms: 4 + 25r2 = -21r Solving 4 + 25r2 = -21r Solving for variable 'r'. Reorder the terms: 4 + 21r + 25r2 = -21r + 21r Combine like terms: -21r + 21r = 0 4 + 21r + 25r2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.16 + 0.84r + r2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + 0.84r + -0.16 + r2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + 0.84r + r2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + 0.84r + r2 = 0 + -0.16 0.84r + r2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 0.84r + r2 = -0.16 The r term is 0.84r. Take half its coefficient (0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. 0.84r + 0.1764 + r2 = -0.16 + 0.1764 Reorder the terms: 0.1764 + 0.84r + r2 = -0.16 + 0.1764 Combine like terms: -0.16 + 0.1764 = 0.0164 0.1764 + 0.84r + r2 = 0.0164 Factor a perfect square on the left side: (r + 0.42)(r + 0.42) = 0.0164 Calculate the square root of the right side: 0.128062485 Break this problem into two subproblems by setting (r + 0.42) equal to 0.128062485 and -0.128062485.Subproblem 1
r + 0.42 = 0.128062485 Simplifying r + 0.42 = 0.128062485 Reorder the terms: 0.42 + r = 0.128062485 Solving 0.42 + r = 0.128062485 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + r = 0.128062485 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + r = 0.128062485 + -0.42 r = 0.128062485 + -0.42 Combine like terms: 0.128062485 + -0.42 = -0.291937515 r = -0.291937515 Simplifying r = -0.291937515Subproblem 2
r + 0.42 = -0.128062485 Simplifying r + 0.42 = -0.128062485 Reorder the terms: 0.42 + r = -0.128062485 Solving 0.42 + r = -0.128062485 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + r = -0.128062485 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + r = -0.128062485 + -0.42 r = -0.128062485 + -0.42 Combine like terms: -0.128062485 + -0.42 = -0.548062485 r = -0.548062485 Simplifying r = -0.548062485Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.291937515, -0.548062485}
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