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Simplifying 2R2 + 7R + -42 = 0 Reorder the terms: -42 + 7R + 2R2 = 0 Solving -42 + 7R + 2R2 = 0 Solving for variable 'R'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + 3.5R + R2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 3.5R + 21 + R2 = 0 + 21 Reorder the terms: -21 + 21 + 3.5R + R2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3.5R + R2 = 0 + 21 3.5R + R2 = 0 + 21 Combine like terms: 0 + 21 = 21 3.5R + R2 = 21 The R term is 3.5R. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5R + 3.0625 + R2 = 21 + 3.0625 Reorder the terms: 3.0625 + 3.5R + R2 = 21 + 3.0625 Combine like terms: 21 + 3.0625 = 24.0625 3.0625 + 3.5R + R2 = 24.0625 Factor a perfect square on the left side: (R + 1.75)(R + 1.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (R + 1.75) equal to 4.905354218 and -4.905354218.Subproblem 1
R + 1.75 = 4.905354218 Simplifying R + 1.75 = 4.905354218 Reorder the terms: 1.75 + R = 4.905354218 Solving 1.75 + R = 4.905354218 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + R = 4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + R = 4.905354218 + -1.75 R = 4.905354218 + -1.75 Combine like terms: 4.905354218 + -1.75 = 3.155354218 R = 3.155354218 Simplifying R = 3.155354218Subproblem 2
R + 1.75 = -4.905354218 Simplifying R + 1.75 = -4.905354218 Reorder the terms: 1.75 + R = -4.905354218 Solving 1.75 + R = -4.905354218 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + R = -4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + R = -4.905354218 + -1.75 R = -4.905354218 + -1.75 Combine like terms: -4.905354218 + -1.75 = -6.655354218 R = -6.655354218 Simplifying R = -6.655354218Solution
The solution to the problem is based on the solutions from the subproblems. R = {3.155354218, -6.655354218}
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