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Simplifying 2x2 + 5.46x + -7.4529 = 0 Reorder the terms: -7.4529 + 5.46x + 2x2 = 0 Solving -7.4529 + 5.46x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.72645 + 2.73x + x2 = 0 Move the constant term to the right: Add '3.72645' to each side of the equation. -3.72645 + 2.73x + 3.72645 + x2 = 0 + 3.72645 Reorder the terms: -3.72645 + 3.72645 + 2.73x + x2 = 0 + 3.72645 Combine like terms: -3.72645 + 3.72645 = 0.00000 0.00000 + 2.73x + x2 = 0 + 3.72645 2.73x + x2 = 0 + 3.72645 Combine like terms: 0 + 3.72645 = 3.72645 2.73x + x2 = 3.72645 The x term is 2.73x. Take half its coefficient (1.365). Square it (1.863225) and add it to both sides. Add '1.863225' to each side of the equation. 2.73x + 1.863225 + x2 = 3.72645 + 1.863225 Reorder the terms: 1.863225 + 2.73x + x2 = 3.72645 + 1.863225 Combine like terms: 3.72645 + 1.863225 = 5.589675 1.863225 + 2.73x + x2 = 5.589675 Factor a perfect square on the left side: (x + 1.365)(x + 1.365) = 5.589675 Calculate the square root of the right side: 2.364249352 Break this problem into two subproblems by setting (x + 1.365) equal to 2.364249352 and -2.364249352.Subproblem 1
x + 1.365 = 2.364249352 Simplifying x + 1.365 = 2.364249352 Reorder the terms: 1.365 + x = 2.364249352 Solving 1.365 + x = 2.364249352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.365' to each side of the equation. 1.365 + -1.365 + x = 2.364249352 + -1.365 Combine like terms: 1.365 + -1.365 = 0.000 0.000 + x = 2.364249352 + -1.365 x = 2.364249352 + -1.365 Combine like terms: 2.364249352 + -1.365 = 0.999249352 x = 0.999249352 Simplifying x = 0.999249352Subproblem 2
x + 1.365 = -2.364249352 Simplifying x + 1.365 = -2.364249352 Reorder the terms: 1.365 + x = -2.364249352 Solving 1.365 + x = -2.364249352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.365' to each side of the equation. 1.365 + -1.365 + x = -2.364249352 + -1.365 Combine like terms: 1.365 + -1.365 = 0.000 0.000 + x = -2.364249352 + -1.365 x = -2.364249352 + -1.365 Combine like terms: -2.364249352 + -1.365 = -3.729249352 x = -3.729249352 Simplifying x = -3.729249352Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.999249352, -3.729249352}
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