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Simplifying 5r2 + 13r + -3 = 0 Reorder the terms: -3 + 13r + 5r2 = 0 Solving -3 + 13r + 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'. -0.6 + 2.6r + r2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2.6r + 0.6 + r2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2.6r + r2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2.6r + r2 = 0 + 0.6 2.6r + r2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2.6r + r2 = 0.6 The r term is 2.6r. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6r + 1.69 + r2 = 0.6 + 1.69 Reorder the terms: 1.69 + 2.6r + r2 = 0.6 + 1.69 Combine like terms: 0.6 + 1.69 = 2.29 1.69 + 2.6r + r2 = 2.29 Factor a perfect square on the left side: (r + 1.3)(r + 1.3) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (r + 1.3) equal to 1.513274595 and -1.513274595.Subproblem 1
r + 1.3 = 1.513274595 Simplifying r + 1.3 = 1.513274595 Reorder the terms: 1.3 + r = 1.513274595 Solving 1.3 + r = 1.513274595 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + r = 1.513274595 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + r = 1.513274595 + -1.3 r = 1.513274595 + -1.3 Combine like terms: 1.513274595 + -1.3 = 0.213274595 r = 0.213274595 Simplifying r = 0.213274595Subproblem 2
r + 1.3 = -1.513274595 Simplifying r + 1.3 = -1.513274595 Reorder the terms: 1.3 + r = -1.513274595 Solving 1.3 + r = -1.513274595 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + r = -1.513274595 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + r = -1.513274595 + -1.3 r = -1.513274595 + -1.3 Combine like terms: -1.513274595 + -1.3 = -2.813274595 r = -2.813274595 Simplifying r = -2.813274595Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.213274595, -2.813274595}
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