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Simplifying 0.770 = ((1 + -1x)(2 + -1x)) Multiply (1 + -1x) * (2 + -1x) 0.770 = ((1(2 + -1x) + -1x * (2 + -1x))) 0.770 = (((2 * 1 + -1x * 1) + -1x * (2 + -1x))) 0.770 = (((2 + -1x) + -1x * (2 + -1x))) 0.770 = ((2 + -1x + (2 * -1x + -1x * -1x))) 0.770 = ((2 + -1x + (-2x + 1x2))) Combine like terms: -1x + -2x = -3x 0.770 = ((2 + -3x + 1x2)) 0.770 = (2 + -3x + 1x2) Remove parenthesis around (2 + -3x + 1x2) 0.770 = 2 + -3x + 1x2 Solving 0.770 = 2 + -3x + 1x2 Solving for variable 'x'. Combine like terms: 0.770 + -2 = -1.23 -1.23 + 3x + -1x2 = 2 + -3x + 1x2 + -2 + 3x + -1x2 Reorder the terms: -1.23 + 3x + -1x2 = 2 + -2 + -3x + 3x + 1x2 + -1x2 Combine like terms: 2 + -2 = 0 -1.23 + 3x + -1x2 = 0 + -3x + 3x + 1x2 + -1x2 -1.23 + 3x + -1x2 = -3x + 3x + 1x2 + -1x2 Combine like terms: -3x + 3x = 0 -1.23 + 3x + -1x2 = 0 + 1x2 + -1x2 -1.23 + 3x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -1.23 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1.23 + -3x + x2 = 0 Move the constant term to the right: Add '-1.23' to each side of the equation. 1.23 + -3x + -1.23 + x2 = 0 + -1.23 Reorder the terms: 1.23 + -1.23 + -3x + x2 = 0 + -1.23 Combine like terms: 1.23 + -1.23 = 0.00 0.00 + -3x + x2 = 0 + -1.23 -3x + x2 = 0 + -1.23 Combine like terms: 0 + -1.23 = -1.23 -3x + x2 = -1.23 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.23 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.23 + 2.25 Combine like terms: -1.23 + 2.25 = 1.02 2.25 + -3x + x2 = 1.02 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.02 Calculate the square root of the right side: 1.009950494 Break this problem into two subproblems by setting (x + -1.5) equal to 1.009950494 and -1.009950494.Subproblem 1
x + -1.5 = 1.009950494 Simplifying x + -1.5 = 1.009950494 Reorder the terms: -1.5 + x = 1.009950494 Solving -1.5 + x = 1.009950494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.009950494 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.009950494 + 1.5 x = 1.009950494 + 1.5 Combine like terms: 1.009950494 + 1.5 = 2.509950494 x = 2.509950494 Simplifying x = 2.509950494Subproblem 2
x + -1.5 = -1.009950494 Simplifying x + -1.5 = -1.009950494 Reorder the terms: -1.5 + x = -1.009950494 Solving -1.5 + x = -1.009950494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.009950494 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.009950494 + 1.5 x = -1.009950494 + 1.5 Combine like terms: -1.009950494 + 1.5 = 0.490049506 x = 0.490049506 Simplifying x = 0.490049506Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.509950494, 0.490049506}
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