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Simplifying 9r2 + -6r + -10 = 0 Reorder the terms: -10 + -6r + 9r2 = 0 Solving -10 + -6r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -0.6666666667r + r2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.6666666667r + 1.111111111 + r2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.6666666667r + r2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.6666666667r + r2 = 0 + 1.111111111 -0.6666666667r + r2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.6666666667r + r2 = 1.111111111 The r term is -0.6666666667r. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667r + 0.1111111112 + r2 = 1.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667r + r2 = 1.111111111 + 0.1111111112 Combine like terms: 1.111111111 + 0.1111111112 = 1.2222222222 0.1111111112 + -0.6666666667r + r2 = 1.2222222222 Factor a perfect square on the left side: (r + -0.3333333334)(r + -0.3333333334) = 1.2222222222 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (r + -0.3333333334) equal to 1.105541597 and -1.105541597.Subproblem 1
r + -0.3333333334 = 1.105541597 Simplifying r + -0.3333333334 = 1.105541597 Reorder the terms: -0.3333333334 + r = 1.105541597 Solving -0.3333333334 + r = 1.105541597 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + r = 1.105541597 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + r = 1.105541597 + 0.3333333334 r = 1.105541597 + 0.3333333334 Combine like terms: 1.105541597 + 0.3333333334 = 1.4388749304 r = 1.4388749304 Simplifying r = 1.4388749304Subproblem 2
r + -0.3333333334 = -1.105541597 Simplifying r + -0.3333333334 = -1.105541597 Reorder the terms: -0.3333333334 + r = -1.105541597 Solving -0.3333333334 + r = -1.105541597 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + r = -1.105541597 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + r = -1.105541597 + 0.3333333334 r = -1.105541597 + 0.3333333334 Combine like terms: -1.105541597 + 0.3333333334 = -0.7722082636 r = -0.7722082636 Simplifying r = -0.7722082636Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.4388749304, -0.7722082636}
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