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Simplifying r2 + r + -603 = 0 Reorder the terms: -603 + r + r2 = 0 Solving -603 + r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '603' to each side of the equation. -603 + r + 603 + r2 = 0 + 603 Reorder the terms: -603 + 603 + r + r2 = 0 + 603 Combine like terms: -603 + 603 = 0 0 + r + r2 = 0 + 603 r + r2 = 0 + 603 Combine like terms: 0 + 603 = 603 r + r2 = 603 The r term is r. 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. r + 0.25 + r2 = 603 + 0.25 Reorder the terms: 0.25 + r + r2 = 603 + 0.25 Combine like terms: 603 + 0.25 = 603.25 0.25 + r + r2 = 603.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 603.25 Calculate the square root of the right side: 24.561148182 Break this problem into two subproblems by setting (r + 0.5) equal to 24.561148182 and -24.561148182.Subproblem 1
r + 0.5 = 24.561148182 Simplifying r + 0.5 = 24.561148182 Reorder the terms: 0.5 + r = 24.561148182 Solving 0.5 + r = 24.561148182 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 = 24.561148182 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 24.561148182 + -0.5 r = 24.561148182 + -0.5 Combine like terms: 24.561148182 + -0.5 = 24.061148182 r = 24.061148182 Simplifying r = 24.061148182Subproblem 2
r + 0.5 = -24.561148182 Simplifying r + 0.5 = -24.561148182 Reorder the terms: 0.5 + r = -24.561148182 Solving 0.5 + r = -24.561148182 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 = -24.561148182 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -24.561148182 + -0.5 r = -24.561148182 + -0.5 Combine like terms: -24.561148182 + -0.5 = -25.061148182 r = -25.061148182 Simplifying r = -25.061148182Solution
The solution to the problem is based on the solutions from the subproblems. r = {24.061148182, -25.061148182}
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