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Simplifying R2 + 14R + -82 = 10 Reorder the terms: -82 + 14R + R2 = 10 Solving -82 + 14R + R2 = 10 Solving for variable 'R'. Reorder the terms: -82 + -10 + 14R + R2 = 10 + -10 Combine like terms: -82 + -10 = -92 -92 + 14R + R2 = 10 + -10 Combine like terms: 10 + -10 = 0 -92 + 14R + R2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 14R + 92 + R2 = 0 + 92 Reorder the terms: -92 + 92 + 14R + R2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 14R + R2 = 0 + 92 14R + R2 = 0 + 92 Combine like terms: 0 + 92 = 92 14R + R2 = 92 The R term is 14R. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14R + 49 + R2 = 92 + 49 Reorder the terms: 49 + 14R + R2 = 92 + 49 Combine like terms: 92 + 49 = 141 49 + 14R + R2 = 141 Factor a perfect square on the left side: (R + 7)(R + 7) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (R + 7) equal to 11.874342087 and -11.874342087.Subproblem 1
R + 7 = 11.874342087 Simplifying R + 7 = 11.874342087 Reorder the terms: 7 + R = 11.874342087 Solving 7 + R = 11.874342087 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + R = 11.874342087 + -7 Combine like terms: 7 + -7 = 0 0 + R = 11.874342087 + -7 R = 11.874342087 + -7 Combine like terms: 11.874342087 + -7 = 4.874342087 R = 4.874342087 Simplifying R = 4.874342087Subproblem 2
R + 7 = -11.874342087 Simplifying R + 7 = -11.874342087 Reorder the terms: 7 + R = -11.874342087 Solving 7 + R = -11.874342087 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + R = -11.874342087 + -7 Combine like terms: 7 + -7 = 0 0 + R = -11.874342087 + -7 R = -11.874342087 + -7 Combine like terms: -11.874342087 + -7 = -18.874342087 R = -18.874342087 Simplifying R = -18.874342087Solution
The solution to the problem is based on the solutions from the subproblems. R = {4.874342087, -18.874342087}
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