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Simplifying 4x2 + 378x + -4248.5 = 0 Reorder the terms: -4248.5 + 378x + 4x2 = 0 Solving -4248.5 + 378x + 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'. -1062.125 + 94.5x + x2 = 0 Move the constant term to the right: Add '1062.125' to each side of the equation. -1062.125 + 94.5x + 1062.125 + x2 = 0 + 1062.125 Reorder the terms: -1062.125 + 1062.125 + 94.5x + x2 = 0 + 1062.125 Combine like terms: -1062.125 + 1062.125 = 0.000 0.000 + 94.5x + x2 = 0 + 1062.125 94.5x + x2 = 0 + 1062.125 Combine like terms: 0 + 1062.125 = 1062.125 94.5x + x2 = 1062.125 The x term is 94.5x. Take half its coefficient (47.25). Square it (2232.5625) and add it to both sides. Add '2232.5625' to each side of the equation. 94.5x + 2232.5625 + x2 = 1062.125 + 2232.5625 Reorder the terms: 2232.5625 + 94.5x + x2 = 1062.125 + 2232.5625 Combine like terms: 1062.125 + 2232.5625 = 3294.6875 2232.5625 + 94.5x + x2 = 3294.6875 Factor a perfect square on the left side: (x + 47.25)(x + 47.25) = 3294.6875 Calculate the square root of the right side: 57.399368463 Break this problem into two subproblems by setting (x + 47.25) equal to 57.399368463 and -57.399368463.Subproblem 1
x + 47.25 = 57.399368463 Simplifying x + 47.25 = 57.399368463 Reorder the terms: 47.25 + x = 57.399368463 Solving 47.25 + x = 57.399368463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.25' to each side of the equation. 47.25 + -47.25 + x = 57.399368463 + -47.25 Combine like terms: 47.25 + -47.25 = 0.00 0.00 + x = 57.399368463 + -47.25 x = 57.399368463 + -47.25 Combine like terms: 57.399368463 + -47.25 = 10.149368463 x = 10.149368463 Simplifying x = 10.149368463Subproblem 2
x + 47.25 = -57.399368463 Simplifying x + 47.25 = -57.399368463 Reorder the terms: 47.25 + x = -57.399368463 Solving 47.25 + x = -57.399368463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.25' to each side of the equation. 47.25 + -47.25 + x = -57.399368463 + -47.25 Combine like terms: 47.25 + -47.25 = 0.00 0.00 + x = -57.399368463 + -47.25 x = -57.399368463 + -47.25 Combine like terms: -57.399368463 + -47.25 = -104.649368463 x = -104.649368463 Simplifying x = -104.649368463Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.149368463, -104.649368463}
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