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Simplifying R2 + -4.5R + 4.5 = 0 Reorder the terms: 4.5 + -4.5R + R2 = 0 Solving 4.5 + -4.5R + R2 = 0 Solving for variable 'R'. Begin completing the square. Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -4.5R + -4.5 + R2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -4.5R + R2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -4.5R + R2 = 0 + -4.5 -4.5R + R2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -4.5R + R2 = -4.5 The R term is -4.5R. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5R + 5.0625 + R2 = -4.5 + 5.0625 Reorder the terms: 5.0625 + -4.5R + R2 = -4.5 + 5.0625 Combine like terms: -4.5 + 5.0625 = 0.5625 5.0625 + -4.5R + R2 = 0.5625 Factor a perfect square on the left side: (R + -2.25)(R + -2.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (R + -2.25) equal to 0.75 and -0.75.Subproblem 1
R + -2.25 = 0.75 Simplifying R + -2.25 = 0.75 Reorder the terms: -2.25 + R = 0.75 Solving -2.25 + R = 0.75 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + R = 0.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + R = 0.75 + 2.25 R = 0.75 + 2.25 Combine like terms: 0.75 + 2.25 = 3 R = 3 Simplifying R = 3Subproblem 2
R + -2.25 = -0.75 Simplifying R + -2.25 = -0.75 Reorder the terms: -2.25 + R = -0.75 Solving -2.25 + R = -0.75 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + R = -0.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + R = -0.75 + 2.25 R = -0.75 + 2.25 Combine like terms: -0.75 + 2.25 = 1.5 R = 1.5 Simplifying R = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. R = {3, 1.5}
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