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Simplifying 5r2 + 20r + -61 = 0 Reorder the terms: -61 + 20r + 5r2 = 0 Solving -61 + 20r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.2 + 4r + r2 = 0 Move the constant term to the right: Add '12.2' to each side of the equation. -12.2 + 4r + 12.2 + r2 = 0 + 12.2 Reorder the terms: -12.2 + 12.2 + 4r + r2 = 0 + 12.2 Combine like terms: -12.2 + 12.2 = 0.0 0.0 + 4r + r2 = 0 + 12.2 4r + r2 = 0 + 12.2 Combine like terms: 0 + 12.2 = 12.2 4r + r2 = 12.2 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 12.2 + 4 Reorder the terms: 4 + 4r + r2 = 12.2 + 4 Combine like terms: 12.2 + 4 = 16.2 4 + 4r + r2 = 16.2 Factor a perfect square on the left side: (r + 2)(r + 2) = 16.2 Calculate the square root of the right side: 4.02492236 Break this problem into two subproblems by setting (r + 2) equal to 4.02492236 and -4.02492236.Subproblem 1
r + 2 = 4.02492236 Simplifying r + 2 = 4.02492236 Reorder the terms: 2 + r = 4.02492236 Solving 2 + r = 4.02492236 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 4.02492236 + -2 Combine like terms: 2 + -2 = 0 0 + r = 4.02492236 + -2 r = 4.02492236 + -2 Combine like terms: 4.02492236 + -2 = 2.02492236 r = 2.02492236 Simplifying r = 2.02492236Subproblem 2
r + 2 = -4.02492236 Simplifying r + 2 = -4.02492236 Reorder the terms: 2 + r = -4.02492236 Solving 2 + r = -4.02492236 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -4.02492236 + -2 Combine like terms: 2 + -2 = 0 0 + r = -4.02492236 + -2 r = -4.02492236 + -2 Combine like terms: -4.02492236 + -2 = -6.02492236 r = -6.02492236 Simplifying r = -6.02492236Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.02492236, -6.02492236}
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