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Simplifying 2.97x2 + -7.43x + -4.46 = 0 Reorder the terms: -4.46 + -7.43x + 2.97x2 = 0 Solving -4.46 + -7.43x + 2.97x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.97 the coefficient of the squared term: Divide each side by '2.97'. -1.501683502 + -2.501683502x + x2 = 0 Move the constant term to the right: Add '1.501683502' to each side of the equation. -1.501683502 + -2.501683502x + 1.501683502 + x2 = 0 + 1.501683502 Reorder the terms: -1.501683502 + 1.501683502 + -2.501683502x + x2 = 0 + 1.501683502 Combine like terms: -1.501683502 + 1.501683502 = 0.000000000 0.000000000 + -2.501683502x + x2 = 0 + 1.501683502 -2.501683502x + x2 = 0 + 1.501683502 Combine like terms: 0 + 1.501683502 = 1.501683502 -2.501683502x + x2 = 1.501683502 The x term is -2.501683502x. Take half its coefficient (-1.250841751). Square it (1.564605086) and add it to both sides. Add '1.564605086' to each side of the equation. -2.501683502x + 1.564605086 + x2 = 1.501683502 + 1.564605086 Reorder the terms: 1.564605086 + -2.501683502x + x2 = 1.501683502 + 1.564605086 Combine like terms: 1.501683502 + 1.564605086 = 3.066288588 1.564605086 + -2.501683502x + x2 = 3.066288588 Factor a perfect square on the left side: (x + -1.250841751)(x + -1.250841751) = 3.066288588 Calculate the square root of the right side: 1.751082119 Break this problem into two subproblems by setting (x + -1.250841751) equal to 1.751082119 and -1.751082119.Subproblem 1
x + -1.250841751 = 1.751082119 Simplifying x + -1.250841751 = 1.751082119 Reorder the terms: -1.250841751 + x = 1.751082119 Solving -1.250841751 + x = 1.751082119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.250841751' to each side of the equation. -1.250841751 + 1.250841751 + x = 1.751082119 + 1.250841751 Combine like terms: -1.250841751 + 1.250841751 = 0.000000000 0.000000000 + x = 1.751082119 + 1.250841751 x = 1.751082119 + 1.250841751 Combine like terms: 1.751082119 + 1.250841751 = 3.00192387 x = 3.00192387 Simplifying x = 3.00192387Subproblem 2
x + -1.250841751 = -1.751082119 Simplifying x + -1.250841751 = -1.751082119 Reorder the terms: -1.250841751 + x = -1.751082119 Solving -1.250841751 + x = -1.751082119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.250841751' to each side of the equation. -1.250841751 + 1.250841751 + x = -1.751082119 + 1.250841751 Combine like terms: -1.250841751 + 1.250841751 = 0.000000000 0.000000000 + x = -1.751082119 + 1.250841751 x = -1.751082119 + 1.250841751 Combine like terms: -1.751082119 + 1.250841751 = -0.500240368 x = -0.500240368 Simplifying x = -0.500240368Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.00192387, -0.500240368}
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