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Simplifying 6.79x2 + 3.64x = 4.68 Reorder the terms: 3.64x + 6.79x2 = 4.68 Solving 3.64x + 6.79x2 = 4.68 Solving for variable 'x'. Reorder the terms: -4.68 + 3.64x + 6.79x2 = 4.68 + -4.68 Combine like terms: 4.68 + -4.68 = 0.00 -4.68 + 3.64x + 6.79x2 = 0.00 Begin completing the square. Divide all terms by 6.79 the coefficient of the squared term: Divide each side by '6.79'. -0.6892488954 + 0.5360824742x + x2 = 0 Move the constant term to the right: Add '0.6892488954' to each side of the equation. -0.6892488954 + 0.5360824742x + 0.6892488954 + x2 = 0 + 0.6892488954 Reorder the terms: -0.6892488954 + 0.6892488954 + 0.5360824742x + x2 = 0 + 0.6892488954 Combine like terms: -0.6892488954 + 0.6892488954 = 0.0000000000 0.0000000000 + 0.5360824742x + x2 = 0 + 0.6892488954 0.5360824742x + x2 = 0 + 0.6892488954 Combine like terms: 0 + 0.6892488954 = 0.6892488954 0.5360824742x + x2 = 0.6892488954 The x term is 0.5360824742x. Take half its coefficient (0.2680412371). Square it (0.07184610479) and add it to both sides. Add '0.07184610479' to each side of the equation. 0.5360824742x + 0.07184610479 + x2 = 0.6892488954 + 0.07184610479 Reorder the terms: 0.07184610479 + 0.5360824742x + x2 = 0.6892488954 + 0.07184610479 Combine like terms: 0.6892488954 + 0.07184610479 = 0.76109500019 0.07184610479 + 0.5360824742x + x2 = 0.76109500019 Factor a perfect square on the left side: (x + 0.2680412371)(x + 0.2680412371) = 0.76109500019 Calculate the square root of the right side: 0.872407588 Break this problem into two subproblems by setting (x + 0.2680412371) equal to 0.872407588 and -0.872407588.Subproblem 1
x + 0.2680412371 = 0.872407588 Simplifying x + 0.2680412371 = 0.872407588 Reorder the terms: 0.2680412371 + x = 0.872407588 Solving 0.2680412371 + x = 0.872407588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2680412371' to each side of the equation. 0.2680412371 + -0.2680412371 + x = 0.872407588 + -0.2680412371 Combine like terms: 0.2680412371 + -0.2680412371 = 0.0000000000 0.0000000000 + x = 0.872407588 + -0.2680412371 x = 0.872407588 + -0.2680412371 Combine like terms: 0.872407588 + -0.2680412371 = 0.6043663509 x = 0.6043663509 Simplifying x = 0.6043663509Subproblem 2
x + 0.2680412371 = -0.872407588 Simplifying x + 0.2680412371 = -0.872407588 Reorder the terms: 0.2680412371 + x = -0.872407588 Solving 0.2680412371 + x = -0.872407588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2680412371' to each side of the equation. 0.2680412371 + -0.2680412371 + x = -0.872407588 + -0.2680412371 Combine like terms: 0.2680412371 + -0.2680412371 = 0.0000000000 0.0000000000 + x = -0.872407588 + -0.2680412371 x = -0.872407588 + -0.2680412371 Combine like terms: -0.872407588 + -0.2680412371 = -1.1404488251 x = -1.1404488251 Simplifying x = -1.1404488251Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6043663509, -1.1404488251}
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