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Simplifying (-8r2 + 5r + -1) + (6r2 + -3r + 10) = 0 Reorder the terms: (-1 + 5r + -8r2) + (6r2 + -3r + 10) = 0 Remove parenthesis around (-1 + 5r + -8r2) -1 + 5r + -8r2 + (6r2 + -3r + 10) = 0 Reorder the terms: -1 + 5r + -8r2 + (10 + -3r + 6r2) = 0 Remove parenthesis around (10 + -3r + 6r2) -1 + 5r + -8r2 + 10 + -3r + 6r2 = 0 Reorder the terms: -1 + 10 + 5r + -3r + -8r2 + 6r2 = 0 Combine like terms: -1 + 10 = 9 9 + 5r + -3r + -8r2 + 6r2 = 0 Combine like terms: 5r + -3r = 2r 9 + 2r + -8r2 + 6r2 = 0 Combine like terms: -8r2 + 6r2 = -2r2 9 + 2r + -2r2 = 0 Solving 9 + 2r + -2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -1r + r2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1r + 4.5 + r2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1r + r2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1r + r2 = 0 + 4.5 -1r + r2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1r + r2 = 4.5 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 4.5 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -1r + r2 = 4.75 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (r + -0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
r + -0.5 = 2.179449472 Simplifying r + -0.5 = 2.179449472 Reorder the terms: -0.5 + r = 2.179449472 Solving -0.5 + r = 2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 2.179449472 + 0.5 r = 2.179449472 + 0.5 Combine like terms: 2.179449472 + 0.5 = 2.679449472 r = 2.679449472 Simplifying r = 2.679449472Subproblem 2
r + -0.5 = -2.179449472 Simplifying r + -0.5 = -2.179449472 Reorder the terms: -0.5 + r = -2.179449472 Solving -0.5 + r = -2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -2.179449472 + 0.5 r = -2.179449472 + 0.5 Combine like terms: -2.179449472 + 0.5 = -1.679449472 r = -1.679449472 Simplifying r = -1.679449472Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.679449472, -1.679449472}
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