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Simplifying 5r2 + 24r + -125 = 0 Reorder the terms: -125 + 24r + 5r2 = 0 Solving -125 + 24r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25 + 4.8r + r2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 4.8r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + 4.8r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4.8r + r2 = 0 + 25 4.8r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 4.8r + r2 = 25 The r term is 4.8r. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8r + 5.76 + r2 = 25 + 5.76 Reorder the terms: 5.76 + 4.8r + r2 = 25 + 5.76 Combine like terms: 25 + 5.76 = 30.76 5.76 + 4.8r + r2 = 30.76 Factor a perfect square on the left side: (r + 2.4)(r + 2.4) = 30.76 Calculate the square root of the right side: 5.54616985 Break this problem into two subproblems by setting (r + 2.4) equal to 5.54616985 and -5.54616985.Subproblem 1
r + 2.4 = 5.54616985 Simplifying r + 2.4 = 5.54616985 Reorder the terms: 2.4 + r = 5.54616985 Solving 2.4 + r = 5.54616985 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = 5.54616985 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = 5.54616985 + -2.4 r = 5.54616985 + -2.4 Combine like terms: 5.54616985 + -2.4 = 3.14616985 r = 3.14616985 Simplifying r = 3.14616985Subproblem 2
r + 2.4 = -5.54616985 Simplifying r + 2.4 = -5.54616985 Reorder the terms: 2.4 + r = -5.54616985 Solving 2.4 + r = -5.54616985 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = -5.54616985 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = -5.54616985 + -2.4 r = -5.54616985 + -2.4 Combine like terms: -5.54616985 + -2.4 = -7.94616985 r = -7.94616985 Simplifying r = -7.94616985Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.14616985, -7.94616985}
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