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Simplifying 2.5x2 + 12x = 3480 Reorder the terms: 12x + 2.5x2 = 3480 Solving 12x + 2.5x2 = 3480 Solving for variable 'x'. Reorder the terms: -3480 + 12x + 2.5x2 = 3480 + -3480 Combine like terms: 3480 + -3480 = 0 -3480 + 12x + 2.5x2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -1392 + 4.8x + x2 = 0 Move the constant term to the right: Add '1392' to each side of the equation. -1392 + 4.8x + 1392 + x2 = 0 + 1392 Reorder the terms: -1392 + 1392 + 4.8x + x2 = 0 + 1392 Combine like terms: -1392 + 1392 = 0 0 + 4.8x + x2 = 0 + 1392 4.8x + x2 = 0 + 1392 Combine like terms: 0 + 1392 = 1392 4.8x + x2 = 1392 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 1392 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 1392 + 5.76 Combine like terms: 1392 + 5.76 = 1397.76 5.76 + 4.8x + x2 = 1397.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 1397.76 Calculate the square root of the right side: 37.386628626 Break this problem into two subproblems by setting (x + 2.4) equal to 37.386628626 and -37.386628626.Subproblem 1
x + 2.4 = 37.386628626 Simplifying x + 2.4 = 37.386628626 Reorder the terms: 2.4 + x = 37.386628626 Solving 2.4 + x = 37.386628626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 37.386628626 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 37.386628626 + -2.4 x = 37.386628626 + -2.4 Combine like terms: 37.386628626 + -2.4 = 34.986628626 x = 34.986628626 Simplifying x = 34.986628626Subproblem 2
x + 2.4 = -37.386628626 Simplifying x + 2.4 = -37.386628626 Reorder the terms: 2.4 + x = -37.386628626 Solving 2.4 + x = -37.386628626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -37.386628626 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -37.386628626 + -2.4 x = -37.386628626 + -2.4 Combine like terms: -37.386628626 + -2.4 = -39.786628626 x = -39.786628626 Simplifying x = -39.786628626Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.986628626, -39.786628626}
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