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Simplifying 9.39(1.6 + -1x)(2.4 + -1x) = 0 Multiply (1.6 + -1x) * (2.4 + -1x) 9.39(1.6(2.4 + -1x) + -1x * (2.4 + -1x)) = 0 9.39((2.4 * 1.6 + -1x * 1.6) + -1x * (2.4 + -1x)) = 0 9.39((3.84 + -1.6x) + -1x * (2.4 + -1x)) = 0 9.39(3.84 + -1.6x + (2.4 * -1x + -1x * -1x)) = 0 9.39(3.84 + -1.6x + (-2.4x + 1x2)) = 0 Combine like terms: -1.6x + -2.4x = -4x 9.39(3.84 + -4x + 1x2) = 0 (3.84 * 9.39 + -4x * 9.39 + 1x2 * 9.39) = 0 (36.0576 + -37.56x + 9.39x2) = 0 Solving 36.0576 + -37.56x + 9.39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.39 the coefficient of the squared term: Divide each side by '9.39'. 3.84 + -4x + x2 = 0 Move the constant term to the right: Add '-3.84' to each side of the equation. 3.84 + -4x + -3.84 + x2 = 0 + -3.84 Reorder the terms: 3.84 + -3.84 + -4x + x2 = 0 + -3.84 Combine like terms: 3.84 + -3.84 = 0.00 0.00 + -4x + x2 = 0 + -3.84 -4x + x2 = 0 + -3.84 Combine like terms: 0 + -3.84 = -3.84 -4x + x2 = -3.84 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.84 + 4 Reorder the terms: 4 + -4x + x2 = -3.84 + 4 Combine like terms: -3.84 + 4 = 0.16 4 + -4x + x2 = 0.16 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -2) equal to 0.4 and -0.4.Subproblem 1
x + -2 = 0.4 Simplifying x + -2 = 0.4 Reorder the terms: -2 + x = 0.4 Solving -2 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.4 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.4 + 2 x = 0.4 + 2 Combine like terms: 0.4 + 2 = 2.4 x = 2.4 Simplifying x = 2.4Subproblem 2
x + -2 = -0.4 Simplifying x + -2 = -0.4 Reorder the terms: -2 + x = -0.4 Solving -2 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.4 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.4 + 2 x = -0.4 + 2 Combine like terms: -0.4 + 2 = 1.6 x = 1.6 Simplifying x = 1.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4, 1.6}
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