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Simplifying 5r * 5r = 26r + 24 Reorder the terms for easier multiplication: 5 * 5r * r = 26r + 24 Multiply 5 * 5 25r * r = 26r + 24 Multiply r * r 25r2 = 26r + 24 Reorder the terms: 25r2 = 24 + 26r Solving 25r2 = 24 + 26r Solving for variable 'r'. Reorder the terms: -24 + -26r + 25r2 = 24 + 26r + -24 + -26r Reorder the terms: -24 + -26r + 25r2 = 24 + -24 + 26r + -26r Combine like terms: 24 + -24 = 0 -24 + -26r + 25r2 = 0 + 26r + -26r -24 + -26r + 25r2 = 26r + -26r Combine like terms: 26r + -26r = 0 -24 + -26r + 25r2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.96 + -1.04r + r2 = 0 Move the constant term to the right: Add '0.96' to each side of the equation. -0.96 + -1.04r + 0.96 + r2 = 0 + 0.96 Reorder the terms: -0.96 + 0.96 + -1.04r + r2 = 0 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + -1.04r + r2 = 0 + 0.96 -1.04r + r2 = 0 + 0.96 Combine like terms: 0 + 0.96 = 0.96 -1.04r + r2 = 0.96 The r term is -1.04r. Take half its coefficient (-0.52). Square it (0.2704) and add it to both sides. Add '0.2704' to each side of the equation. -1.04r + 0.2704 + r2 = 0.96 + 0.2704 Reorder the terms: 0.2704 + -1.04r + r2 = 0.96 + 0.2704 Combine like terms: 0.96 + 0.2704 = 1.2304 0.2704 + -1.04r + r2 = 1.2304 Factor a perfect square on the left side: (r + -0.52)(r + -0.52) = 1.2304 Calculate the square root of the right side: 1.10923397 Break this problem into two subproblems by setting (r + -0.52) equal to 1.10923397 and -1.10923397.Subproblem 1
r + -0.52 = 1.10923397 Simplifying r + -0.52 = 1.10923397 Reorder the terms: -0.52 + r = 1.10923397 Solving -0.52 + r = 1.10923397 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + r = 1.10923397 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + r = 1.10923397 + 0.52 r = 1.10923397 + 0.52 Combine like terms: 1.10923397 + 0.52 = 1.62923397 r = 1.62923397 Simplifying r = 1.62923397Subproblem 2
r + -0.52 = -1.10923397 Simplifying r + -0.52 = -1.10923397 Reorder the terms: -0.52 + r = -1.10923397 Solving -0.52 + r = -1.10923397 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + r = -1.10923397 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + r = -1.10923397 + 0.52 r = -1.10923397 + 0.52 Combine like terms: -1.10923397 + 0.52 = -0.58923397 r = -0.58923397 Simplifying r = -0.58923397Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.62923397, -0.58923397}
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