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Simplifying 5r2 + -3r + -4 = 0 Reorder the terms: -4 + -3r + 5r2 = 0 Solving -4 + -3r + 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'. -0.8 + -0.6r + r2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6r + 0.8 + r2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6r + r2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6r + r2 = 0 + 0.8 -0.6r + r2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6r + r2 = 0.8 The r term is -0.6r. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6r + 0.09 + r2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6r + r2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6r + r2 = 0.89 Factor a perfect square on the left side: (r + -0.3)(r + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (r + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
r + -0.3 = 0.943398113 Simplifying r + -0.3 = 0.943398113 Reorder the terms: -0.3 + r = 0.943398113 Solving -0.3 + r = 0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + r = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + r = 0.943398113 + 0.3 r = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 r = 1.243398113 Simplifying r = 1.243398113Subproblem 2
r + -0.3 = -0.943398113 Simplifying r + -0.3 = -0.943398113 Reorder the terms: -0.3 + r = -0.943398113 Solving -0.3 + r = -0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + r = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + r = -0.943398113 + 0.3 r = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 r = -0.643398113 Simplifying r = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.243398113, -0.643398113}
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