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Simplifying r2 + -484 = r Reorder the terms: -484 + r2 = r Solving -484 + r2 = r Solving for variable 'r'. Reorder the terms: -484 + -1r + r2 = r + -1r Combine like terms: r + -1r = 0 -484 + -1r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '484' to each side of the equation. -484 + -1r + 484 + r2 = 0 + 484 Reorder the terms: -484 + 484 + -1r + r2 = 0 + 484 Combine like terms: -484 + 484 = 0 0 + -1r + r2 = 0 + 484 -1r + r2 = 0 + 484 Combine like terms: 0 + 484 = 484 -1r + r2 = 484 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 484 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 484 + 0.25 Combine like terms: 484 + 0.25 = 484.25 0.25 + -1r + r2 = 484.25 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 484.25 Calculate the square root of the right side: 22.005681085 Break this problem into two subproblems by setting (r + -0.5) equal to 22.005681085 and -22.005681085.Subproblem 1
r + -0.5 = 22.005681085 Simplifying r + -0.5 = 22.005681085 Reorder the terms: -0.5 + r = 22.005681085 Solving -0.5 + r = 22.005681085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 22.005681085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 22.005681085 + 0.5 r = 22.005681085 + 0.5 Combine like terms: 22.005681085 + 0.5 = 22.505681085 r = 22.505681085 Simplifying r = 22.505681085Subproblem 2
r + -0.5 = -22.005681085 Simplifying r + -0.5 = -22.005681085 Reorder the terms: -0.5 + r = -22.005681085 Solving -0.5 + r = -22.005681085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -22.005681085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -22.005681085 + 0.5 r = -22.005681085 + 0.5 Combine like terms: -22.005681085 + 0.5 = -21.505681085 r = -21.505681085 Simplifying r = -21.505681085Solution
The solution to the problem is based on the solutions from the subproblems. r = {22.505681085, -21.505681085}
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