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Simplifying 5r2 + 25r = 45 Reorder the terms: 25r + 5r2 = 45 Solving 25r + 5r2 = 45 Solving for variable 'r'. Reorder the terms: -45 + 25r + 5r2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 25r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 5r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 5r + r2)' equal to zero and attempt to solve: Simplifying -9 + 5r + r2 = 0 Solving -9 + 5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 5r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + 5r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5r + r2 = 0 + 9 5r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 5r + r2 = 9 The r term is 5r. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5r + 6.25 + r2 = 9 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + 5r + r2 = 15.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (r + 2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
r + 2.5 = 3.905124838 Simplifying r + 2.5 = 3.905124838 Reorder the terms: 2.5 + r = 3.905124838 Solving 2.5 + r = 3.905124838 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 3.905124838 + -2.5 r = 3.905124838 + -2.5 Combine like terms: 3.905124838 + -2.5 = 1.405124838 r = 1.405124838 Simplifying r = 1.405124838Subproblem 2
r + 2.5 = -3.905124838 Simplifying r + 2.5 = -3.905124838 Reorder the terms: 2.5 + r = -3.905124838 Solving 2.5 + r = -3.905124838 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -3.905124838 + -2.5 r = -3.905124838 + -2.5 Combine like terms: -3.905124838 + -2.5 = -6.405124838 r = -6.405124838 Simplifying r = -6.405124838Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.405124838, -6.405124838}Solution
r = {1.405124838, -6.405124838}
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