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Simplifying 5r2 + 24r + -1 = 0 Reorder the terms: -1 + 24r + 5r2 = 0 Solving -1 + 24r + 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'. -0.2 + 4.8r + r2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 4.8r + 0.2 + r2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 4.8r + r2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 4.8r + r2 = 0 + 0.2 4.8r + r2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 4.8r + r2 = 0.2 The r term is 4.8r. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8r + 5.76 + r2 = 0.2 + 5.76 Reorder the terms: 5.76 + 4.8r + r2 = 0.2 + 5.76 Combine like terms: 0.2 + 5.76 = 5.96 5.76 + 4.8r + r2 = 5.96 Factor a perfect square on the left side: (r + 2.4)(r + 2.4) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (r + 2.4) equal to 2.441311123 and -2.441311123.Subproblem 1
r + 2.4 = 2.441311123 Simplifying r + 2.4 = 2.441311123 Reorder the terms: 2.4 + r = 2.441311123 Solving 2.4 + r = 2.441311123 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = 2.441311123 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = 2.441311123 + -2.4 r = 2.441311123 + -2.4 Combine like terms: 2.441311123 + -2.4 = 0.041311123 r = 0.041311123 Simplifying r = 0.041311123Subproblem 2
r + 2.4 = -2.441311123 Simplifying r + 2.4 = -2.441311123 Reorder the terms: 2.4 + r = -2.441311123 Solving 2.4 + r = -2.441311123 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = -2.441311123 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = -2.441311123 + -2.4 r = -2.441311123 + -2.4 Combine like terms: -2.441311123 + -2.4 = -4.841311123 r = -4.841311123 Simplifying r = -4.841311123Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.041311123, -4.841311123}
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