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Simplifying 2.4x2 + 9x = 330 Reorder the terms: 9x + 2.4x2 = 330 Solving 9x + 2.4x2 = 330 Solving for variable 'x'. Reorder the terms: -330 + 9x + 2.4x2 = 330 + -330 Combine like terms: 330 + -330 = 0 -330 + 9x + 2.4x2 = 0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -137.5 + 3.75x + x2 = 0 Move the constant term to the right: Add '137.5' to each side of the equation. -137.5 + 3.75x + 137.5 + x2 = 0 + 137.5 Reorder the terms: -137.5 + 137.5 + 3.75x + x2 = 0 + 137.5 Combine like terms: -137.5 + 137.5 = 0.0 0.0 + 3.75x + x2 = 0 + 137.5 3.75x + x2 = 0 + 137.5 Combine like terms: 0 + 137.5 = 137.5 3.75x + x2 = 137.5 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 137.5 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 137.5 + 3.515625 Combine like terms: 137.5 + 3.515625 = 141.015625 3.515625 + 3.75x + x2 = 141.015625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 141.015625 Calculate the square root of the right side: 11.875 Break this problem into two subproblems by setting (x + 1.875) equal to 11.875 and -11.875.Subproblem 1
x + 1.875 = 11.875 Simplifying x + 1.875 = 11.875 Reorder the terms: 1.875 + x = 11.875 Solving 1.875 + x = 11.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 11.875 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 11.875 + -1.875 x = 11.875 + -1.875 Combine like terms: 11.875 + -1.875 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 1.875 = -11.875 Simplifying x + 1.875 = -11.875 Reorder the terms: 1.875 + x = -11.875 Solving 1.875 + x = -11.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -11.875 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -11.875 + -1.875 x = -11.875 + -1.875 Combine like terms: -11.875 + -1.875 = -13.75 x = -13.75 Simplifying x = -13.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -13.75}
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