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Simplifying r2 + -7r + -6 = r + -3 Reorder the terms: -6 + -7r + r2 = r + -3 Reorder the terms: -6 + -7r + r2 = -3 + r Solving -6 + -7r + r2 = -3 + r Solving for variable 'r'. Reorder the terms: -6 + 3 + -7r + -1r + r2 = -3 + r + 3 + -1r Combine like terms: -6 + 3 = -3 -3 + -7r + -1r + r2 = -3 + r + 3 + -1r Combine like terms: -7r + -1r = -8r -3 + -8r + r2 = -3 + r + 3 + -1r Reorder the terms: -3 + -8r + r2 = -3 + 3 + r + -1r Combine like terms: -3 + 3 = 0 -3 + -8r + r2 = 0 + r + -1r -3 + -8r + r2 = r + -1r Combine like terms: r + -1r = 0 -3 + -8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + -8r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8r + r2 = 0 + 3 -8r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8r + r2 = 3 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = 3 + 16 Reorder the terms: 16 + -8r + r2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8r + r2 = 19 Factor a perfect square on the left side: (r + -4)(r + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (r + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
r + -4 = 4.358898944 Simplifying r + -4 = 4.358898944 Reorder the terms: -4 + r = 4.358898944 Solving -4 + r = 4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + r = 4.358898944 + 4 r = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 r = 8.358898944 Simplifying r = 8.358898944Subproblem 2
r + -4 = -4.358898944 Simplifying r + -4 = -4.358898944 Reorder the terms: -4 + r = -4.358898944 Solving -4 + r = -4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + r = -4.358898944 + 4 r = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 r = -0.358898944 Simplifying r = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.358898944, -0.358898944}
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