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Simplifying 4x2 + 33x + 61 = 0 Reorder the terms: 61 + 33x + 4x2 = 0 Solving 61 + 33x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.25 + 8.25x + x2 = 0 Move the constant term to the right: Add '-15.25' to each side of the equation. 15.25 + 8.25x + -15.25 + x2 = 0 + -15.25 Reorder the terms: 15.25 + -15.25 + 8.25x + x2 = 0 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + 8.25x + x2 = 0 + -15.25 8.25x + x2 = 0 + -15.25 Combine like terms: 0 + -15.25 = -15.25 8.25x + x2 = -15.25 The x term is 8.25x. Take half its coefficient (4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. 8.25x + 17.015625 + x2 = -15.25 + 17.015625 Reorder the terms: 17.015625 + 8.25x + x2 = -15.25 + 17.015625 Combine like terms: -15.25 + 17.015625 = 1.765625 17.015625 + 8.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + 4.125)(x + 4.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + 4.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x + 4.125 = 1.328768227 Simplifying x + 4.125 = 1.328768227 Reorder the terms: 4.125 + x = 1.328768227 Solving 4.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = 1.328768227 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = 1.328768227 + -4.125 x = 1.328768227 + -4.125 Combine like terms: 1.328768227 + -4.125 = -2.796231773 x = -2.796231773 Simplifying x = -2.796231773Subproblem 2
x + 4.125 = -1.328768227 Simplifying x + 4.125 = -1.328768227 Reorder the terms: 4.125 + x = -1.328768227 Solving 4.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = -1.328768227 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = -1.328768227 + -4.125 x = -1.328768227 + -4.125 Combine like terms: -1.328768227 + -4.125 = -5.453768227 x = -5.453768227 Simplifying x = -5.453768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.796231773, -5.453768227}
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