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Simplifying (6r2 + 5r + -12) + (-5r2 + -13r + 6) = 0 Reorder the terms: (-12 + 5r + 6r2) + (-5r2 + -13r + 6) = 0 Remove parenthesis around (-12 + 5r + 6r2) -12 + 5r + 6r2 + (-5r2 + -13r + 6) = 0 Reorder the terms: -12 + 5r + 6r2 + (6 + -13r + -5r2) = 0 Remove parenthesis around (6 + -13r + -5r2) -12 + 5r + 6r2 + 6 + -13r + -5r2 = 0 Reorder the terms: -12 + 6 + 5r + -13r + 6r2 + -5r2 = 0 Combine like terms: -12 + 6 = -6 -6 + 5r + -13r + 6r2 + -5r2 = 0 Combine like terms: 5r + -13r = -8r -6 + -8r + 6r2 + -5r2 = 0 Combine like terms: 6r2 + -5r2 = 1r2 -6 + -8r + 1r2 = 0 Solving -6 + -8r + 1r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -8r + 6 + r2 = 0 + 6 Reorder the terms: -6 + 6 + -8r + r2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8r + r2 = 0 + 6 -8r + r2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8r + r2 = 6 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 = 6 + 16 Reorder the terms: 16 + -8r + r2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8r + r2 = 22 Factor a perfect square on the left side: (r + -4)(r + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (r + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
r + -4 = 4.69041576 Simplifying r + -4 = 4.69041576 Reorder the terms: -4 + r = 4.69041576 Solving -4 + r = 4.69041576 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 = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + r = 4.69041576 + 4 r = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 r = 8.69041576 Simplifying r = 8.69041576Subproblem 2
r + -4 = -4.69041576 Simplifying r + -4 = -4.69041576 Reorder the terms: -4 + r = -4.69041576 Solving -4 + r = -4.69041576 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 = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + r = -4.69041576 + 4 r = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 r = -0.69041576 Simplifying r = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.69041576, -0.69041576}
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