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Simplifying 2r2 + -10r + -25 = 0 Reorder the terms: -25 + -10r + 2r2 = 0 Solving -25 + -10r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -5r + r2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -5r + 12.5 + r2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -5r + r2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -5r + r2 = 0 + 12.5 -5r + r2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -5r + r2 = 12.5 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 = 12.5 + 6.25 Reorder the terms: 6.25 + -5r + r2 = 12.5 + 6.25 Combine like terms: 12.5 + 6.25 = 18.75 6.25 + -5r + r2 = 18.75 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (r + -2.5) equal to 4.330127019 and -4.330127019.Subproblem 1
r + -2.5 = 4.330127019 Simplifying r + -2.5 = 4.330127019 Reorder the terms: -2.5 + r = 4.330127019 Solving -2.5 + r = 4.330127019 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 = 4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 4.330127019 + 2.5 r = 4.330127019 + 2.5 Combine like terms: 4.330127019 + 2.5 = 6.830127019 r = 6.830127019 Simplifying r = 6.830127019Subproblem 2
r + -2.5 = -4.330127019 Simplifying r + -2.5 = -4.330127019 Reorder the terms: -2.5 + r = -4.330127019 Solving -2.5 + r = -4.330127019 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 = -4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -4.330127019 + 2.5 r = -4.330127019 + 2.5 Combine like terms: -4.330127019 + 2.5 = -1.830127019 r = -1.830127019 Simplifying r = -1.830127019Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.830127019, -1.830127019}
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