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Simplifying 4x2 + 9x + -46 = 0 Reorder the terms: -46 + 9x + 4x2 = 0 Solving -46 + 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'. -11.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 2.25x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 2.25x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 2.25x + x2 = 0 + 11.5 2.25x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 2.25x + x2 = 11.5 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 = 11.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 11.5 + 1.265625 Combine like terms: 11.5 + 1.265625 = 12.765625 1.265625 + 2.25x + x2 = 12.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 12.765625 Calculate the square root of the right side: 3.572901482 Break this problem into two subproblems by setting (x + 1.125) equal to 3.572901482 and -3.572901482.Subproblem 1
x + 1.125 = 3.572901482 Simplifying x + 1.125 = 3.572901482 Reorder the terms: 1.125 + x = 3.572901482 Solving 1.125 + x = 3.572901482 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 = 3.572901482 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 3.572901482 + -1.125 x = 3.572901482 + -1.125 Combine like terms: 3.572901482 + -1.125 = 2.447901482 x = 2.447901482 Simplifying x = 2.447901482Subproblem 2
x + 1.125 = -3.572901482 Simplifying x + 1.125 = -3.572901482 Reorder the terms: 1.125 + x = -3.572901482 Solving 1.125 + x = -3.572901482 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 = -3.572901482 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -3.572901482 + -1.125 x = -3.572901482 + -1.125 Combine like terms: -3.572901482 + -1.125 = -4.697901482 x = -4.697901482 Simplifying x = -4.697901482Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.447901482, -4.697901482}
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