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Simplifying R2 + -4R + -19 = 7 Reorder the terms: -19 + -4R + R2 = 7 Solving -19 + -4R + R2 = 7 Solving for variable 'R'. Reorder the terms: -19 + -7 + -4R + R2 = 7 + -7 Combine like terms: -19 + -7 = -26 -26 + -4R + R2 = 7 + -7 Combine like terms: 7 + -7 = 0 -26 + -4R + R2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -4R + 26 + R2 = 0 + 26 Reorder the terms: -26 + 26 + -4R + R2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -4R + R2 = 0 + 26 -4R + R2 = 0 + 26 Combine like terms: 0 + 26 = 26 -4R + R2 = 26 The R term is -4R. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4R + 4 + R2 = 26 + 4 Reorder the terms: 4 + -4R + R2 = 26 + 4 Combine like terms: 26 + 4 = 30 4 + -4R + R2 = 30 Factor a perfect square on the left side: (R + -2)(R + -2) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (R + -2) equal to 5.477225575 and -5.477225575.Subproblem 1
R + -2 = 5.477225575 Simplifying R + -2 = 5.477225575 Reorder the terms: -2 + R = 5.477225575 Solving -2 + R = 5.477225575 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + R = 5.477225575 + 2 Combine like terms: -2 + 2 = 0 0 + R = 5.477225575 + 2 R = 5.477225575 + 2 Combine like terms: 5.477225575 + 2 = 7.477225575 R = 7.477225575 Simplifying R = 7.477225575Subproblem 2
R + -2 = -5.477225575 Simplifying R + -2 = -5.477225575 Reorder the terms: -2 + R = -5.477225575 Solving -2 + R = -5.477225575 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + R = -5.477225575 + 2 Combine like terms: -2 + 2 = 0 0 + R = -5.477225575 + 2 R = -5.477225575 + 2 Combine like terms: -5.477225575 + 2 = -3.477225575 R = -3.477225575 Simplifying R = -3.477225575Solution
The solution to the problem is based on the solutions from the subproblems. R = {7.477225575, -3.477225575}
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