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Simplifying 9r2 + 17r + -3 = 0 Reorder the terms: -3 + 17r + 9r2 = 0 Solving -3 + 17r + 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'. -0.3333333333 + 1.888888889r + r2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.888888889r + 0.3333333333 + r2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.888888889r + r2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.888888889r + r2 = 0 + 0.3333333333 1.888888889r + r2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.888888889r + r2 = 0.3333333333 The r term is 1.888888889r. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889r + 0.8919753087 + r2 = 0.3333333333 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889r + r2 = 0.3333333333 + 0.8919753087 Combine like terms: 0.3333333333 + 0.8919753087 = 1.225308642 0.8919753087 + 1.888888889r + r2 = 1.225308642 Factor a perfect square on the left side: (r + 0.9444444445)(r + 0.9444444445) = 1.225308642 Calculate the square root of the right side: 1.106936603 Break this problem into two subproblems by setting (r + 0.9444444445) equal to 1.106936603 and -1.106936603.Subproblem 1
r + 0.9444444445 = 1.106936603 Simplifying r + 0.9444444445 = 1.106936603 Reorder the terms: 0.9444444445 + r = 1.106936603 Solving 0.9444444445 + r = 1.106936603 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + r = 1.106936603 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + r = 1.106936603 + -0.9444444445 r = 1.106936603 + -0.9444444445 Combine like terms: 1.106936603 + -0.9444444445 = 0.1624921585 r = 0.1624921585 Simplifying r = 0.1624921585Subproblem 2
r + 0.9444444445 = -1.106936603 Simplifying r + 0.9444444445 = -1.106936603 Reorder the terms: 0.9444444445 + r = -1.106936603 Solving 0.9444444445 + r = -1.106936603 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + r = -1.106936603 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + r = -1.106936603 + -0.9444444445 r = -1.106936603 + -0.9444444445 Combine like terms: -1.106936603 + -0.9444444445 = -2.0513810475 r = -2.0513810475 Simplifying r = -2.0513810475Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.1624921585, -2.0513810475}
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