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Simplifying 5r2 + -12r + -5 = 0 Reorder the terms: -5 + -12r + 5r2 = 0 Solving -5 + -12r + 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'. -1 + -2.4r + r2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.4r + 1 + r2 = 0 + 1 Reorder the terms: -1 + 1 + -2.4r + r2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.4r + r2 = 0 + 1 -2.4r + r2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.4r + r2 = 1 The r term is -2.4r. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4r + 1.44 + r2 = 1 + 1.44 Reorder the terms: 1.44 + -2.4r + r2 = 1 + 1.44 Combine like terms: 1 + 1.44 = 2.44 1.44 + -2.4r + r2 = 2.44 Factor a perfect square on the left side: (r + -1.2)(r + -1.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (r + -1.2) equal to 1.562049935 and -1.562049935.Subproblem 1
r + -1.2 = 1.562049935 Simplifying r + -1.2 = 1.562049935 Reorder the terms: -1.2 + r = 1.562049935 Solving -1.2 + r = 1.562049935 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + r = 1.562049935 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + r = 1.562049935 + 1.2 r = 1.562049935 + 1.2 Combine like terms: 1.562049935 + 1.2 = 2.762049935 r = 2.762049935 Simplifying r = 2.762049935Subproblem 2
r + -1.2 = -1.562049935 Simplifying r + -1.2 = -1.562049935 Reorder the terms: -1.2 + r = -1.562049935 Solving -1.2 + r = -1.562049935 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + r = -1.562049935 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + r = -1.562049935 + 1.2 r = -1.562049935 + 1.2 Combine like terms: -1.562049935 + 1.2 = -0.362049935 r = -0.362049935 Simplifying r = -0.362049935Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.762049935, -0.362049935}
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