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Simplifying r2 + -12r + -38 = 10 Reorder the terms: -38 + -12r + r2 = 10 Solving -38 + -12r + r2 = 10 Solving for variable 'r'. Reorder the terms: -38 + -10 + -12r + r2 = 10 + -10 Combine like terms: -38 + -10 = -48 -48 + -12r + r2 = 10 + -10 Combine like terms: 10 + -10 = 0 -48 + -12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -12r + 48 + r2 = 0 + 48 Reorder the terms: -48 + 48 + -12r + r2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -12r + r2 = 0 + 48 -12r + r2 = 0 + 48 Combine like terms: 0 + 48 = 48 -12r + r2 = 48 The r term is -12r. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12r + 36 + r2 = 48 + 36 Reorder the terms: 36 + -12r + r2 = 48 + 36 Combine like terms: 48 + 36 = 84 36 + -12r + r2 = 84 Factor a perfect square on the left side: (r + -6)(r + -6) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (r + -6) equal to 9.16515139 and -9.16515139.Subproblem 1
r + -6 = 9.16515139 Simplifying r + -6 = 9.16515139 Reorder the terms: -6 + r = 9.16515139 Solving -6 + r = 9.16515139 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + r = 9.16515139 + 6 r = 9.16515139 + 6 Combine like terms: 9.16515139 + 6 = 15.16515139 r = 15.16515139 Simplifying r = 15.16515139Subproblem 2
r + -6 = -9.16515139 Simplifying r + -6 = -9.16515139 Reorder the terms: -6 + r = -9.16515139 Solving -6 + r = -9.16515139 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + r = -9.16515139 + 6 r = -9.16515139 + 6 Combine like terms: -9.16515139 + 6 = -3.16515139 r = -3.16515139 Simplifying r = -3.16515139Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.16515139, -3.16515139}
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