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Simplifying 35x2 = 414x + 2 Reorder the terms: 35x2 = 2 + 414x Solving 35x2 = 2 + 414x Solving for variable 'x'. Reorder the terms: -2 + -414x + 35x2 = 2 + 414x + -2 + -414x Reorder the terms: -2 + -414x + 35x2 = 2 + -2 + 414x + -414x Combine like terms: 2 + -2 = 0 -2 + -414x + 35x2 = 0 + 414x + -414x -2 + -414x + 35x2 = 414x + -414x Combine like terms: 414x + -414x = 0 -2 + -414x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.05714285714 + -11.82857143x + x2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -11.82857143x + 0.05714285714 + x2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -11.82857143x + x2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -11.82857143x + x2 = 0 + 0.05714285714 -11.82857143x + x2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -11.82857143x + x2 = 0.05714285714 The x term is -11.82857143x. Take half its coefficient (-5.914285715). Square it (34.97877552) and add it to both sides. Add '34.97877552' to each side of the equation. -11.82857143x + 34.97877552 + x2 = 0.05714285714 + 34.97877552 Reorder the terms: 34.97877552 + -11.82857143x + x2 = 0.05714285714 + 34.97877552 Combine like terms: 0.05714285714 + 34.97877552 = 35.03591837714 34.97877552 + -11.82857143x + x2 = 35.03591837714 Factor a perfect square on the left side: (x + -5.914285715)(x + -5.914285715) = 35.03591837714 Calculate the square root of the right side: 5.919114662 Break this problem into two subproblems by setting (x + -5.914285715) equal to 5.919114662 and -5.919114662.Subproblem 1
x + -5.914285715 = 5.919114662 Simplifying x + -5.914285715 = 5.919114662 Reorder the terms: -5.914285715 + x = 5.919114662 Solving -5.914285715 + x = 5.919114662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.914285715' to each side of the equation. -5.914285715 + 5.914285715 + x = 5.919114662 + 5.914285715 Combine like terms: -5.914285715 + 5.914285715 = 0.000000000 0.000000000 + x = 5.919114662 + 5.914285715 x = 5.919114662 + 5.914285715 Combine like terms: 5.919114662 + 5.914285715 = 11.833400377 x = 11.833400377 Simplifying x = 11.833400377Subproblem 2
x + -5.914285715 = -5.919114662 Simplifying x + -5.914285715 = -5.919114662 Reorder the terms: -5.914285715 + x = -5.919114662 Solving -5.914285715 + x = -5.919114662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.914285715' to each side of the equation. -5.914285715 + 5.914285715 + x = -5.919114662 + 5.914285715 Combine like terms: -5.914285715 + 5.914285715 = 0.000000000 0.000000000 + x = -5.919114662 + 5.914285715 x = -5.919114662 + 5.914285715 Combine like terms: -5.919114662 + 5.914285715 = -0.004828947 x = -0.004828947 Simplifying x = -0.004828947Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.833400377, -0.004828947}
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