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Simplifying 5r2 + -6r = 6 Reorder the terms: -6r + 5r2 = 6 Solving -6r + 5r2 = 6 Solving for variable 'r'. Reorder the terms: -6 + -6r + 5r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -6r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1.2r + r2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.2r + 1.2 + r2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.2r + r2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.2r + r2 = 0 + 1.2 -1.2r + r2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.2r + r2 = 1.2 The r term is -1.2r. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2r + 0.36 + r2 = 1.2 + 0.36 Reorder the terms: 0.36 + -1.2r + r2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + -1.2r + r2 = 1.56 Factor a perfect square on the left side: (r + -0.6)(r + -0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (r + -0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
r + -0.6 = 1.2489996 Simplifying r + -0.6 = 1.2489996 Reorder the terms: -0.6 + r = 1.2489996 Solving -0.6 + r = 1.2489996 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + r = 1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + r = 1.2489996 + 0.6 r = 1.2489996 + 0.6 Combine like terms: 1.2489996 + 0.6 = 1.8489996 r = 1.8489996 Simplifying r = 1.8489996Subproblem 2
r + -0.6 = -1.2489996 Simplifying r + -0.6 = -1.2489996 Reorder the terms: -0.6 + r = -1.2489996 Solving -0.6 + r = -1.2489996 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + r = -1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + r = -1.2489996 + 0.6 r = -1.2489996 + 0.6 Combine like terms: -1.2489996 + 0.6 = -0.6489996 r = -0.6489996 Simplifying r = -0.6489996Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.8489996, -0.6489996}
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