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Simplifying r2 + -25r + -10 = 0 Reorder the terms: -10 + -25r + r2 = 0 Solving -10 + -25r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -25r + 10 + r2 = 0 + 10 Reorder the terms: -10 + 10 + -25r + r2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -25r + r2 = 0 + 10 -25r + r2 = 0 + 10 Combine like terms: 0 + 10 = 10 -25r + r2 = 10 The r term is -25r. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25r + 156.25 + r2 = 10 + 156.25 Reorder the terms: 156.25 + -25r + r2 = 10 + 156.25 Combine like terms: 10 + 156.25 = 166.25 156.25 + -25r + r2 = 166.25 Factor a perfect square on the left side: (r + -12.5)(r + -12.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (r + -12.5) equal to 12.893796958 and -12.893796958.Subproblem 1
r + -12.5 = 12.893796958 Simplifying r + -12.5 = 12.893796958 Reorder the terms: -12.5 + r = 12.893796958 Solving -12.5 + r = 12.893796958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = 12.893796958 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = 12.893796958 + 12.5 r = 12.893796958 + 12.5 Combine like terms: 12.893796958 + 12.5 = 25.393796958 r = 25.393796958 Simplifying r = 25.393796958Subproblem 2
r + -12.5 = -12.893796958 Simplifying r + -12.5 = -12.893796958 Reorder the terms: -12.5 + r = -12.893796958 Solving -12.5 + r = -12.893796958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = -12.893796958 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = -12.893796958 + 12.5 r = -12.893796958 + 12.5 Combine like terms: -12.893796958 + 12.5 = -0.393796958 r = -0.393796958 Simplifying r = -0.393796958Solution
The solution to the problem is based on the solutions from the subproblems. r = {25.393796958, -0.393796958}
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