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Simplifying R * 1.6(R + 10) * 1.6 = 176 Reorder the terms: R * 1.6(10 + R) * 1.6 = 176 Reorder the terms for easier multiplication: 1.6 * 1.6R(10 + R) = 176 Multiply 1.6 * 1.6 2.56R(10 + R) = 176 (10 * 2.56R + R * 2.56R) = 176 (25.6R + 2.56R2) = 176 Solving 25.6R + 2.56R2 = 176 Solving for variable 'R'. Reorder the terms: -176 + 25.6R + 2.56R2 = 176 + -176 Combine like terms: 176 + -176 = 0 -176 + 25.6R + 2.56R2 = 0 Begin completing the square. Divide all terms by 2.56 the coefficient of the squared term: Divide each side by '2.56'. -68.75 + 10R + R2 = 0 Move the constant term to the right: Add '68.75' to each side of the equation. -68.75 + 10R + 68.75 + R2 = 0 + 68.75 Reorder the terms: -68.75 + 68.75 + 10R + R2 = 0 + 68.75 Combine like terms: -68.75 + 68.75 = 0.00 0.00 + 10R + R2 = 0 + 68.75 10R + R2 = 0 + 68.75 Combine like terms: 0 + 68.75 = 68.75 10R + R2 = 68.75 The R term is 10R. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10R + 25 + R2 = 68.75 + 25 Reorder the terms: 25 + 10R + R2 = 68.75 + 25 Combine like terms: 68.75 + 25 = 93.75 25 + 10R + R2 = 93.75 Factor a perfect square on the left side: (R + 5)(R + 5) = 93.75 Calculate the square root of the right side: 9.682458366 Break this problem into two subproblems by setting (R + 5) equal to 9.682458366 and -9.682458366.Subproblem 1
R + 5 = 9.682458366 Simplifying R + 5 = 9.682458366 Reorder the terms: 5 + R = 9.682458366 Solving 5 + R = 9.682458366 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + R = 9.682458366 + -5 Combine like terms: 5 + -5 = 0 0 + R = 9.682458366 + -5 R = 9.682458366 + -5 Combine like terms: 9.682458366 + -5 = 4.682458366 R = 4.682458366 Simplifying R = 4.682458366Subproblem 2
R + 5 = -9.682458366 Simplifying R + 5 = -9.682458366 Reorder the terms: 5 + R = -9.682458366 Solving 5 + R = -9.682458366 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + R = -9.682458366 + -5 Combine like terms: 5 + -5 = 0 0 + R = -9.682458366 + -5 R = -9.682458366 + -5 Combine like terms: -9.682458366 + -5 = -14.682458366 R = -14.682458366 Simplifying R = -14.682458366Solution
The solution to the problem is based on the solutions from the subproblems. R = {4.682458366, -14.682458366}
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