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Simplifying 4r2 + 4r = 33 Reorder the terms: 4r + 4r2 = 33 Solving 4r + 4r2 = 33 Solving for variable 'r'. Reorder the terms: -33 + 4r + 4r2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 4r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + r + r2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + r + 8.25 + r2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + r + r2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + r + r2 = 0 + 8.25 r + r2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 r + r2 = 8.25 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. + 0.25 + r2 = 8.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 8.25 + 0.25 Combine like terms: 8.25 + 0.25 = 8.5 1.25 + r2 = 8.5 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (r + 0.5) equal to 2.915475947 and -2.915475947.Subproblem 1
r + 0.5 = 2.915475947 Simplifying r + 0.5 = 2.915475947 Reorder the terms: 0.5 + r = 2.915475947 Solving 0.5 + r = 2.915475947 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 = 2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 2.915475947 + -0.5 r = 2.915475947 + -0.5 Combine like terms: 2.915475947 + -0.5 = 2.415475947 r = 2.415475947 Simplifying r = 2.415475947Subproblem 2
r + 0.5 = -2.915475947 Simplifying r + 0.5 = -2.915475947 Reorder the terms: 0.5 + r = -2.915475947 Solving 0.5 + r = -2.915475947 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 = -2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -2.915475947 + -0.5 r = -2.915475947 + -0.5 Combine like terms: -2.915475947 + -0.5 = -3.415475947 r = -3.415475947 Simplifying r = -3.415475947Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.415475947, -3.415475947}
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