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Simplifying 5r2 + 7r + -2 = 0 Reorder the terms: -2 + 7r + 5r2 = 0 Solving -2 + 7r + 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'. -0.4 + 1.4r + r2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.4r + 0.4 + r2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.4r + r2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.4r + r2 = 0 + 0.4 1.4r + r2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.4r + r2 = 0.4 The r term is 1.4r. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4r + 0.49 + r2 = 0.4 + 0.49 Reorder the terms: 0.49 + 1.4r + r2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + 1.4r + r2 = 0.89 Factor a perfect square on the left side: (r + 0.7)(r + 0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (r + 0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
r + 0.7 = 0.943398113 Simplifying r + 0.7 = 0.943398113 Reorder the terms: 0.7 + r = 0.943398113 Solving 0.7 + r = 0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = 0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = 0.943398113 + -0.7 r = 0.943398113 + -0.7 Combine like terms: 0.943398113 + -0.7 = 0.243398113 r = 0.243398113 Simplifying r = 0.243398113Subproblem 2
r + 0.7 = -0.943398113 Simplifying r + 0.7 = -0.943398113 Reorder the terms: 0.7 + r = -0.943398113 Solving 0.7 + r = -0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = -0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = -0.943398113 + -0.7 r = -0.943398113 + -0.7 Combine like terms: -0.943398113 + -0.7 = -1.643398113 r = -1.643398113 Simplifying r = -1.643398113Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.243398113, -1.643398113}
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