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Simplifying 3r2 + -5r + -33 = 0 Reorder the terms: -33 + -5r + 3r2 = 0 Solving -33 + -5r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + -1.666666667r + r2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -1.666666667r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + -1.666666667r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1.666666667r + r2 = 0 + 11 -1.666666667r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1.666666667r + r2 = 11 The r term is -1.666666667r. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667r + 0.6944444447 + r2 = 11 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667r + r2 = 11 + 0.6944444447 Combine like terms: 11 + 0.6944444447 = 11.6944444447 0.6944444447 + -1.666666667r + r2 = 11.6944444447 Factor a perfect square on the left side: (r + -0.8333333335)(r + -0.8333333335) = 11.6944444447 Calculate the square root of the right side: 3.419714088 Break this problem into two subproblems by setting (r + -0.8333333335) equal to 3.419714088 and -3.419714088.Subproblem 1
r + -0.8333333335 = 3.419714088 Simplifying r + -0.8333333335 = 3.419714088 Reorder the terms: -0.8333333335 + r = 3.419714088 Solving -0.8333333335 + r = 3.419714088 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + r = 3.419714088 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + r = 3.419714088 + 0.8333333335 r = 3.419714088 + 0.8333333335 Combine like terms: 3.419714088 + 0.8333333335 = 4.2530474215 r = 4.2530474215 Simplifying r = 4.2530474215Subproblem 2
r + -0.8333333335 = -3.419714088 Simplifying r + -0.8333333335 = -3.419714088 Reorder the terms: -0.8333333335 + r = -3.419714088 Solving -0.8333333335 + r = -3.419714088 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + r = -3.419714088 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + r = -3.419714088 + 0.8333333335 r = -3.419714088 + 0.8333333335 Combine like terms: -3.419714088 + 0.8333333335 = -2.5863807545 r = -2.5863807545 Simplifying r = -2.5863807545Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.2530474215, -2.5863807545}
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