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Simplifying 5r2 + -2r = 12 Reorder the terms: -2r + 5r2 = 12 Solving -2r + 5r2 = 12 Solving for variable 'r'. Reorder the terms: -12 + -2r + 5r2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -2r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -0.4r + r2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.4r + 2.4 + r2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.4r + r2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.4r + r2 = 0 + 2.4 -0.4r + r2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.4r + r2 = 2.4 The r term is -0.4r. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4r + 0.04 + r2 = 2.4 + 0.04 Reorder the terms: 0.04 + -0.4r + r2 = 2.4 + 0.04 Combine like terms: 2.4 + 0.04 = 2.44 0.04 + -0.4r + r2 = 2.44 Factor a perfect square on the left side: (r + -0.2)(r + -0.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (r + -0.2) equal to 1.562049935 and -1.562049935.Subproblem 1
r + -0.2 = 1.562049935 Simplifying r + -0.2 = 1.562049935 Reorder the terms: -0.2 + r = 1.562049935 Solving -0.2 + r = 1.562049935 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + r = 1.562049935 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + r = 1.562049935 + 0.2 r = 1.562049935 + 0.2 Combine like terms: 1.562049935 + 0.2 = 1.762049935 r = 1.762049935 Simplifying r = 1.762049935Subproblem 2
r + -0.2 = -1.562049935 Simplifying r + -0.2 = -1.562049935 Reorder the terms: -0.2 + r = -1.562049935 Solving -0.2 + r = -1.562049935 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + r = -1.562049935 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + r = -1.562049935 + 0.2 r = -1.562049935 + 0.2 Combine like terms: -1.562049935 + 0.2 = -1.362049935 r = -1.362049935 Simplifying r = -1.362049935Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.762049935, -1.362049935}
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