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Simplifying 4r2 + 9r + -8 = 0 Reorder the terms: -8 + 9r + 4r2 = 0 Solving -8 + 9r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 2.25r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.25r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + 2.25r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.25r + r2 = 0 + 2 2.25r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.25r + r2 = 2 The r term is 2.25r. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25r + 1.265625 + r2 = 2 + 1.265625 Reorder the terms: 1.265625 + 2.25r + r2 = 2 + 1.265625 Combine like terms: 2 + 1.265625 = 3.265625 1.265625 + 2.25r + r2 = 3.265625 Factor a perfect square on the left side: (r + 1.125)(r + 1.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (r + 1.125) equal to 1.807104037 and -1.807104037.Subproblem 1
r + 1.125 = 1.807104037 Simplifying r + 1.125 = 1.807104037 Reorder the terms: 1.125 + r = 1.807104037 Solving 1.125 + r = 1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + r = 1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + r = 1.807104037 + -1.125 r = 1.807104037 + -1.125 Combine like terms: 1.807104037 + -1.125 = 0.682104037 r = 0.682104037 Simplifying r = 0.682104037Subproblem 2
r + 1.125 = -1.807104037 Simplifying r + 1.125 = -1.807104037 Reorder the terms: 1.125 + r = -1.807104037 Solving 1.125 + r = -1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + r = -1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + r = -1.807104037 + -1.125 r = -1.807104037 + -1.125 Combine like terms: -1.807104037 + -1.125 = -2.932104037 r = -2.932104037 Simplifying r = -2.932104037Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.682104037, -2.932104037}
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