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Simplifying 4x2 + 71x + 204 = 0 Reorder the terms: 204 + 71x + 4x2 = 0 Solving 204 + 71x + 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'. 51 + 17.75x + x2 = 0 Move the constant term to the right: Add '-51' to each side of the equation. 51 + 17.75x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + 17.75x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 17.75x + x2 = 0 + -51 17.75x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 17.75x + x2 = -51 The x term is 17.75x. Take half its coefficient (8.875). Square it (78.765625) and add it to both sides. Add '78.765625' to each side of the equation. 17.75x + 78.765625 + x2 = -51 + 78.765625 Reorder the terms: 78.765625 + 17.75x + x2 = -51 + 78.765625 Combine like terms: -51 + 78.765625 = 27.765625 78.765625 + 17.75x + x2 = 27.765625 Factor a perfect square on the left side: (x + 8.875)(x + 8.875) = 27.765625 Calculate the square root of the right side: 5.269309727 Break this problem into two subproblems by setting (x + 8.875) equal to 5.269309727 and -5.269309727.Subproblem 1
x + 8.875 = 5.269309727 Simplifying x + 8.875 = 5.269309727 Reorder the terms: 8.875 + x = 5.269309727 Solving 8.875 + x = 5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.875' to each side of the equation. 8.875 + -8.875 + x = 5.269309727 + -8.875 Combine like terms: 8.875 + -8.875 = 0.000 0.000 + x = 5.269309727 + -8.875 x = 5.269309727 + -8.875 Combine like terms: 5.269309727 + -8.875 = -3.605690273 x = -3.605690273 Simplifying x = -3.605690273Subproblem 2
x + 8.875 = -5.269309727 Simplifying x + 8.875 = -5.269309727 Reorder the terms: 8.875 + x = -5.269309727 Solving 8.875 + x = -5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.875' to each side of the equation. 8.875 + -8.875 + x = -5.269309727 + -8.875 Combine like terms: 8.875 + -8.875 = 0.000 0.000 + x = -5.269309727 + -8.875 x = -5.269309727 + -8.875 Combine like terms: -5.269309727 + -8.875 = -14.144309727 x = -14.144309727 Simplifying x = -14.144309727Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.605690273, -14.144309727}
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