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Simplifying 3x2 = -9.6x + -5.5 Reorder the terms: 3x2 = -5.5 + -9.6x Solving 3x2 = -5.5 + -9.6x Solving for variable 'x'. Reorder the terms: 5.5 + 9.6x + 3x2 = -5.5 + -9.6x + 5.5 + 9.6x Reorder the terms: 5.5 + 9.6x + 3x2 = -5.5 + 5.5 + -9.6x + 9.6x Combine like terms: -5.5 + 5.5 = 0.0 5.5 + 9.6x + 3x2 = 0.0 + -9.6x + 9.6x 5.5 + 9.6x + 3x2 = -9.6x + 9.6x Combine like terms: -9.6x + 9.6x = 0.0 5.5 + 9.6x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.833333333 + 3.2x + x2 = 0.0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + 3.2x + -1.833333333 + x2 = 0.0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + 3.2x + x2 = 0.0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + 3.2x + x2 = 0.0 + -1.833333333 3.2x + x2 = 0.0 + -1.833333333 Combine like terms: 0.0 + -1.833333333 = -1.833333333 3.2x + x2 = -1.833333333 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -1.833333333 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -1.833333333 + 2.56 Combine like terms: -1.833333333 + 2.56 = 0.726666667 2.56 + 3.2x + x2 = 0.726666667 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 0.726666667 Calculate the square root of the right side: 0.852447457 Break this problem into two subproblems by setting (x + 1.6) equal to 0.852447457 and -0.852447457.Subproblem 1
x + 1.6 = 0.852447457 Simplifying x + 1.6 = 0.852447457 Reorder the terms: 1.6 + x = 0.852447457 Solving 1.6 + x = 0.852447457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 0.852447457 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 0.852447457 + -1.6 x = 0.852447457 + -1.6 Combine like terms: 0.852447457 + -1.6 = -0.747552543 x = -0.747552543 Simplifying x = -0.747552543Subproblem 2
x + 1.6 = -0.852447457 Simplifying x + 1.6 = -0.852447457 Reorder the terms: 1.6 + x = -0.852447457 Solving 1.6 + x = -0.852447457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -0.852447457 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -0.852447457 + -1.6 x = -0.852447457 + -1.6 Combine like terms: -0.852447457 + -1.6 = -2.452447457 x = -2.452447457 Simplifying x = -2.452447457Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.747552543, -2.452447457}
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