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Simplifying 13r2 + 21r + -10 = 9 Reorder the terms: -10 + 21r + 13r2 = 9 Solving -10 + 21r + 13r2 = 9 Solving for variable 'r'. Reorder the terms: -10 + -9 + 21r + 13r2 = 9 + -9 Combine like terms: -10 + -9 = -19 -19 + 21r + 13r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -19 + 21r + 13r2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.461538462 + 1.615384615r + r2 = 0 Move the constant term to the right: Add '1.461538462' to each side of the equation. -1.461538462 + 1.615384615r + 1.461538462 + r2 = 0 + 1.461538462 Reorder the terms: -1.461538462 + 1.461538462 + 1.615384615r + r2 = 0 + 1.461538462 Combine like terms: -1.461538462 + 1.461538462 = 0.000000000 0.000000000 + 1.615384615r + r2 = 0 + 1.461538462 1.615384615r + r2 = 0 + 1.461538462 Combine like terms: 0 + 1.461538462 = 1.461538462 1.615384615r + r2 = 1.461538462 The r term is 1.615384615r. Take half its coefficient (0.8076923075). Square it (0.6523668636) and add it to both sides. Add '0.6523668636' to each side of the equation. 1.615384615r + 0.6523668636 + r2 = 1.461538462 + 0.6523668636 Reorder the terms: 0.6523668636 + 1.615384615r + r2 = 1.461538462 + 0.6523668636 Combine like terms: 1.461538462 + 0.6523668636 = 2.1139053256 0.6523668636 + 1.615384615r + r2 = 2.1139053256 Factor a perfect square on the left side: (r + 0.8076923075)(r + 0.8076923075) = 2.1139053256 Calculate the square root of the right side: 1.453927552 Break this problem into two subproblems by setting (r + 0.8076923075) equal to 1.453927552 and -1.453927552.Subproblem 1
r + 0.8076923075 = 1.453927552 Simplifying r + 0.8076923075 = 1.453927552 Reorder the terms: 0.8076923075 + r = 1.453927552 Solving 0.8076923075 + r = 1.453927552 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.8076923075' to each side of the equation. 0.8076923075 + -0.8076923075 + r = 1.453927552 + -0.8076923075 Combine like terms: 0.8076923075 + -0.8076923075 = 0.0000000000 0.0000000000 + r = 1.453927552 + -0.8076923075 r = 1.453927552 + -0.8076923075 Combine like terms: 1.453927552 + -0.8076923075 = 0.6462352445 r = 0.6462352445 Simplifying r = 0.6462352445Subproblem 2
r + 0.8076923075 = -1.453927552 Simplifying r + 0.8076923075 = -1.453927552 Reorder the terms: 0.8076923075 + r = -1.453927552 Solving 0.8076923075 + r = -1.453927552 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.8076923075' to each side of the equation. 0.8076923075 + -0.8076923075 + r = -1.453927552 + -0.8076923075 Combine like terms: 0.8076923075 + -0.8076923075 = 0.0000000000 0.0000000000 + r = -1.453927552 + -0.8076923075 r = -1.453927552 + -0.8076923075 Combine like terms: -1.453927552 + -0.8076923075 = -2.2616198595 r = -2.2616198595 Simplifying r = -2.2616198595Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.6462352445, -2.2616198595}
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