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Simplifying 5r2 + 21r + -10 = 0 Reorder the terms: -10 + 21r + 5r2 = 0 Solving -10 + 21r + 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'. -2 + 4.2r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.2r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + 4.2r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.2r + r2 = 0 + 2 4.2r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.2r + r2 = 2 The r term is 4.2r. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2r + 4.41 + r2 = 2 + 4.41 Reorder the terms: 4.41 + 4.2r + r2 = 2 + 4.41 Combine like terms: 2 + 4.41 = 6.41 4.41 + 4.2r + r2 = 6.41 Factor a perfect square on the left side: (r + 2.1)(r + 2.1) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (r + 2.1) equal to 2.53179778 and -2.53179778.Subproblem 1
r + 2.1 = 2.53179778 Simplifying r + 2.1 = 2.53179778 Reorder the terms: 2.1 + r = 2.53179778 Solving 2.1 + r = 2.53179778 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + r = 2.53179778 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + r = 2.53179778 + -2.1 r = 2.53179778 + -2.1 Combine like terms: 2.53179778 + -2.1 = 0.43179778 r = 0.43179778 Simplifying r = 0.43179778Subproblem 2
r + 2.1 = -2.53179778 Simplifying r + 2.1 = -2.53179778 Reorder the terms: 2.1 + r = -2.53179778 Solving 2.1 + r = -2.53179778 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + r = -2.53179778 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + r = -2.53179778 + -2.1 r = -2.53179778 + -2.1 Combine like terms: -2.53179778 + -2.1 = -4.63179778 r = -4.63179778 Simplifying r = -4.63179778Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.43179778, -4.63179778}
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