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Simplifying 4r2 + -1r + -201 = 0 Reorder the terms: -201 + -1r + 4r2 = 0 Solving -201 + -1r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -50.25 + -0.25r + r2 = 0 Move the constant term to the right: Add '50.25' to each side of the equation. -50.25 + -0.25r + 50.25 + r2 = 0 + 50.25 Reorder the terms: -50.25 + 50.25 + -0.25r + r2 = 0 + 50.25 Combine like terms: -50.25 + 50.25 = 0.00 0.00 + -0.25r + r2 = 0 + 50.25 -0.25r + r2 = 0 + 50.25 Combine like terms: 0 + 50.25 = 50.25 -0.25r + r2 = 50.25 The r term is -0.25r. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25r + 0.015625 + r2 = 50.25 + 0.015625 Reorder the terms: 0.015625 + -0.25r + r2 = 50.25 + 0.015625 Combine like terms: 50.25 + 0.015625 = 50.265625 0.015625 + -0.25r + r2 = 50.265625 Factor a perfect square on the left side: (r + -0.125)(r + -0.125) = 50.265625 Calculate the square root of the right side: 7.089825456 Break this problem into two subproblems by setting (r + -0.125) equal to 7.089825456 and -7.089825456.Subproblem 1
r + -0.125 = 7.089825456 Simplifying r + -0.125 = 7.089825456 Reorder the terms: -0.125 + r = 7.089825456 Solving -0.125 + r = 7.089825456 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + r = 7.089825456 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = 7.089825456 + 0.125 r = 7.089825456 + 0.125 Combine like terms: 7.089825456 + 0.125 = 7.214825456 r = 7.214825456 Simplifying r = 7.214825456Subproblem 2
r + -0.125 = -7.089825456 Simplifying r + -0.125 = -7.089825456 Reorder the terms: -0.125 + r = -7.089825456 Solving -0.125 + r = -7.089825456 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + r = -7.089825456 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = -7.089825456 + 0.125 r = -7.089825456 + 0.125 Combine like terms: -7.089825456 + 0.125 = -6.964825456 r = -6.964825456 Simplifying r = -6.964825456Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.214825456, -6.964825456}
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