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Simplifying 4x2 + 9x + -7056 = 0 Reorder the terms: -7056 + 9x + 4x2 = 0 Solving -7056 + 9x + 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'. -1764 + 2.25x + x2 = 0 Move the constant term to the right: Add '1764' to each side of the equation. -1764 + 2.25x + 1764 + x2 = 0 + 1764 Reorder the terms: -1764 + 1764 + 2.25x + x2 = 0 + 1764 Combine like terms: -1764 + 1764 = 0 0 + 2.25x + x2 = 0 + 1764 2.25x + x2 = 0 + 1764 Combine like terms: 0 + 1764 = 1764 2.25x + x2 = 1764 The x term is 2.25x. 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. 2.25x + 1.265625 + x2 = 1764 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 1764 + 1.265625 Combine like terms: 1764 + 1.265625 = 1765.265625 1.265625 + 2.25x + x2 = 1765.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 1765.265625 Calculate the square root of the right side: 42.015064263 Break this problem into two subproblems by setting (x + 1.125) equal to 42.015064263 and -42.015064263.Subproblem 1
x + 1.125 = 42.015064263 Simplifying x + 1.125 = 42.015064263 Reorder the terms: 1.125 + x = 42.015064263 Solving 1.125 + x = 42.015064263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 42.015064263 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 42.015064263 + -1.125 x = 42.015064263 + -1.125 Combine like terms: 42.015064263 + -1.125 = 40.890064263 x = 40.890064263 Simplifying x = 40.890064263Subproblem 2
x + 1.125 = -42.015064263 Simplifying x + 1.125 = -42.015064263 Reorder the terms: 1.125 + x = -42.015064263 Solving 1.125 + x = -42.015064263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -42.015064263 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -42.015064263 + -1.125 x = -42.015064263 + -1.125 Combine like terms: -42.015064263 + -1.125 = -43.140064263 x = -43.140064263 Simplifying x = -43.140064263Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.890064263, -43.140064263}
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