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Simplifying 3.71(4.8 + -1x)(1.2 + -1x) = 0 Multiply (4.8 + -1x) * (1.2 + -1x) 3.71(4.8(1.2 + -1x) + -1x * (1.2 + -1x)) = 0 3.71((1.2 * 4.8 + -1x * 4.8) + -1x * (1.2 + -1x)) = 0 3.71((5.76 + -4.8x) + -1x * (1.2 + -1x)) = 0 3.71(5.76 + -4.8x + (1.2 * -1x + -1x * -1x)) = 0 3.71(5.76 + -4.8x + (-1.2x + 1x2)) = 0 Combine like terms: -4.8x + -1.2x = -6x 3.71(5.76 + -6x + 1x2) = 0 (5.76 * 3.71 + -6x * 3.71 + 1x2 * 3.71) = 0 (21.3696 + -22.26x + 3.71x2) = 0 Solving 21.3696 + -22.26x + 3.71x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.71 the coefficient of the squared term: Divide each side by '3.71'. 5.76 + -6x + x2 = 0 Move the constant term to the right: Add '-5.76' to each side of the equation. 5.76 + -6x + -5.76 + x2 = 0 + -5.76 Reorder the terms: 5.76 + -5.76 + -6x + x2 = 0 + -5.76 Combine like terms: 5.76 + -5.76 = 0.00 0.00 + -6x + x2 = 0 + -5.76 -6x + x2 = 0 + -5.76 Combine like terms: 0 + -5.76 = -5.76 -6x + x2 = -5.76 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.76 + 9 Reorder the terms: 9 + -6x + x2 = -5.76 + 9 Combine like terms: -5.76 + 9 = 3.24 9 + -6x + x2 = 3.24 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.24 Calculate the square root of the right side: 1.8 Break this problem into two subproblems by setting (x + -3) equal to 1.8 and -1.8.Subproblem 1
x + -3 = 1.8 Simplifying x + -3 = 1.8 Reorder the terms: -3 + x = 1.8 Solving -3 + x = 1.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.8 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.8 + 3 x = 1.8 + 3 Combine like terms: 1.8 + 3 = 4.8 x = 4.8 Simplifying x = 4.8Subproblem 2
x + -3 = -1.8 Simplifying x + -3 = -1.8 Reorder the terms: -3 + x = -1.8 Solving -3 + x = -1.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.8 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.8 + 3 x = -1.8 + 3 Combine like terms: -1.8 + 3 = 1.2 x = 1.2 Simplifying x = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8, 1.2}
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