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Simplifying 5r2 + -6 = -4r Reorder the terms: -6 + 5r2 = -4r Solving -6 + 5r2 = -4r Solving for variable 'r'. Reorder the terms: -6 + 4r + 5r2 = -4r + 4r Combine like terms: -4r + 4r = 0 -6 + 4r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 0.8r + r2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.8r + 1.2 + r2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.8r + r2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.8r + r2 = 0 + 1.2 0.8r + r2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.8r + r2 = 1.2 The r term is 0.8r. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8r + 0.16 + r2 = 1.2 + 0.16 Reorder the terms: 0.16 + 0.8r + r2 = 1.2 + 0.16 Combine like terms: 1.2 + 0.16 = 1.36 0.16 + 0.8r + r2 = 1.36 Factor a perfect square on the left side: (r + 0.4)(r + 0.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (r + 0.4) equal to 1.166190379 and -1.166190379.Subproblem 1
r + 0.4 = 1.166190379 Simplifying r + 0.4 = 1.166190379 Reorder the terms: 0.4 + r = 1.166190379 Solving 0.4 + r = 1.166190379 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + r = 1.166190379 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + r = 1.166190379 + -0.4 r = 1.166190379 + -0.4 Combine like terms: 1.166190379 + -0.4 = 0.766190379 r = 0.766190379 Simplifying r = 0.766190379Subproblem 2
r + 0.4 = -1.166190379 Simplifying r + 0.4 = -1.166190379 Reorder the terms: 0.4 + r = -1.166190379 Solving 0.4 + r = -1.166190379 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + r = -1.166190379 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + r = -1.166190379 + -0.4 r = -1.166190379 + -0.4 Combine like terms: -1.166190379 + -0.4 = -1.566190379 r = -1.566190379 Simplifying r = -1.566190379Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.766190379, -1.566190379}
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