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Simplifying 25 + -1r2 = 4r Solving 25 + -1r2 = 4r Solving for variable 'r'. Reorder the terms: 25 + -4r + -1r2 = 4r + -4r Combine like terms: 4r + -4r = 0 25 + -4r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 4r + r2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 4r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + 4r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4r + r2 = 0 + 25 4r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 4r + r2 = 25 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 25 + 4 Reorder the terms: 4 + 4r + r2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4r + r2 = 29 Factor a perfect square on the left side: (r + 2)(r + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (r + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
r + 2 = 5.385164807 Simplifying r + 2 = 5.385164807 Reorder the terms: 2 + r = 5.385164807 Solving 2 + r = 5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + r = 5.385164807 + -2 r = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 r = 3.385164807 Simplifying r = 3.385164807Subproblem 2
r + 2 = -5.385164807 Simplifying r + 2 = -5.385164807 Reorder the terms: 2 + r = -5.385164807 Solving 2 + r = -5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + r = -5.385164807 + -2 r = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 r = -7.385164807 Simplifying r = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.385164807, -7.385164807}
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