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Simplifying -5r2 + 8r + 2 = 0 Reorder the terms: 2 + 8r + -5r2 = 0 Solving 2 + 8r + -5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -1.6r + r2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.6r + 0.4 + r2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.6r + r2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.6r + r2 = 0 + 0.4 -1.6r + r2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.6r + r2 = 0.4 The r term is -1.6r. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6r + 0.64 + r2 = 0.4 + 0.64 Reorder the terms: 0.64 + -1.6r + r2 = 0.4 + 0.64 Combine like terms: 0.4 + 0.64 = 1.04 0.64 + -1.6r + r2 = 1.04 Factor a perfect square on the left side: (r + -0.8)(r + -0.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (r + -0.8) equal to 1.019803903 and -1.019803903.Subproblem 1
r + -0.8 = 1.019803903 Simplifying r + -0.8 = 1.019803903 Reorder the terms: -0.8 + r = 1.019803903 Solving -0.8 + r = 1.019803903 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + r = 1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + r = 1.019803903 + 0.8 r = 1.019803903 + 0.8 Combine like terms: 1.019803903 + 0.8 = 1.819803903 r = 1.819803903 Simplifying r = 1.819803903Subproblem 2
r + -0.8 = -1.019803903 Simplifying r + -0.8 = -1.019803903 Reorder the terms: -0.8 + r = -1.019803903 Solving -0.8 + r = -1.019803903 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + r = -1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + r = -1.019803903 + 0.8 r = -1.019803903 + 0.8 Combine like terms: -1.019803903 + 0.8 = -0.219803903 r = -0.219803903 Simplifying r = -0.219803903Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.819803903, -0.219803903}
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