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Simplifying 4r2 + -7r + -16 = 0 Reorder the terms: -16 + -7r + 4r2 = 0 Solving -16 + -7r + 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'. -4 + -1.75r + r2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.75r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + -1.75r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.75r + r2 = 0 + 4 -1.75r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.75r + r2 = 4 The r term is -1.75r. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75r + 0.765625 + r2 = 4 + 0.765625 Reorder the terms: 0.765625 + -1.75r + r2 = 4 + 0.765625 Combine like terms: 4 + 0.765625 = 4.765625 0.765625 + -1.75r + r2 = 4.765625 Factor a perfect square on the left side: (r + -0.875)(r + -0.875) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (r + -0.875) equal to 2.18303115 and -2.18303115.Subproblem 1
r + -0.875 = 2.18303115 Simplifying r + -0.875 = 2.18303115 Reorder the terms: -0.875 + r = 2.18303115 Solving -0.875 + r = 2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = 2.18303115 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = 2.18303115 + 0.875 r = 2.18303115 + 0.875 Combine like terms: 2.18303115 + 0.875 = 3.05803115 r = 3.05803115 Simplifying r = 3.05803115Subproblem 2
r + -0.875 = -2.18303115 Simplifying r + -0.875 = -2.18303115 Reorder the terms: -0.875 + r = -2.18303115 Solving -0.875 + r = -2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = -2.18303115 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = -2.18303115 + 0.875 r = -2.18303115 + 0.875 Combine like terms: -2.18303115 + 0.875 = -1.30803115 r = -1.30803115 Simplifying r = -1.30803115Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.05803115, -1.30803115}
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