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Simplifying 2x2 + 3x = 380 Reorder the terms: 3x + 2x2 = 380 Solving 3x + 2x2 = 380 Solving for variable 'x'. Reorder the terms: -380 + 3x + 2x2 = 380 + -380 Combine like terms: 380 + -380 = 0 -380 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -190 + 1.5x + x2 = 0 Move the constant term to the right: Add '190' to each side of the equation. -190 + 1.5x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 1.5x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 1.5x + x2 = 0 + 190 1.5x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 1.5x + x2 = 190 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 190 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 190 + 0.5625 Combine like terms: 190 + 0.5625 = 190.5625 0.5625 + 1.5x + x2 = 190.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 190.5625 Calculate the square root of the right side: 13.804437692 Break this problem into two subproblems by setting (x + 0.75) equal to 13.804437692 and -13.804437692.Subproblem 1
x + 0.75 = 13.804437692 Simplifying x + 0.75 = 13.804437692 Reorder the terms: 0.75 + x = 13.804437692 Solving 0.75 + x = 13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 13.804437692 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 13.804437692 + -0.75 x = 13.804437692 + -0.75 Combine like terms: 13.804437692 + -0.75 = 13.054437692 x = 13.054437692 Simplifying x = 13.054437692Subproblem 2
x + 0.75 = -13.804437692 Simplifying x + 0.75 = -13.804437692 Reorder the terms: 0.75 + x = -13.804437692 Solving 0.75 + x = -13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -13.804437692 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -13.804437692 + -0.75 x = -13.804437692 + -0.75 Combine like terms: -13.804437692 + -0.75 = -14.554437692 x = -14.554437692 Simplifying x = -14.554437692Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.054437692, -14.554437692}
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