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Simplifying -4(-3x + 8) * 3x = -5 Reorder the terms: -4(8 + -3x) * 3x = -5 Reorder the terms for easier multiplication: -4 * 3x(8 + -3x) = -5 Multiply -4 * 3 -12x(8 + -3x) = -5 (8 * -12x + -3x * -12x) = -5 (-96x + 36x2) = -5 Solving -96x + 36x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + -96x + 36x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -96x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.1388888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.1388888889' to each side of the equation. 0.1388888889 + -2.666666667x + -0.1388888889 + x2 = 0 + -0.1388888889 Reorder the terms: 0.1388888889 + -0.1388888889 + -2.666666667x + x2 = 0 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + -0.1388888889 -2.666666667x + x2 = 0 + -0.1388888889 Combine like terms: 0 + -0.1388888889 = -0.1388888889 -2.666666667x + x2 = -0.1388888889 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -0.1388888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -0.1388888889 + 1.777777780 Combine like terms: -0.1388888889 + 1.777777780 = 1.6388888911 1.777777780 + -2.666666667x + x2 = 1.6388888911 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.6388888911 Calculate the square root of the right side: 1.280190959 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.280190959 and -1.280190959.Subproblem 1
x + -1.333333334 = 1.280190959 Simplifying x + -1.333333334 = 1.280190959 Reorder the terms: -1.333333334 + x = 1.280190959 Solving -1.333333334 + x = 1.280190959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.280190959 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.280190959 + 1.333333334 x = 1.280190959 + 1.333333334 Combine like terms: 1.280190959 + 1.333333334 = 2.613524293 x = 2.613524293 Simplifying x = 2.613524293Subproblem 2
x + -1.333333334 = -1.280190959 Simplifying x + -1.333333334 = -1.280190959 Reorder the terms: -1.333333334 + x = -1.280190959 Solving -1.333333334 + x = -1.280190959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.280190959 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.280190959 + 1.333333334 x = -1.280190959 + 1.333333334 Combine like terms: -1.280190959 + 1.333333334 = 0.053142375 x = 0.053142375 Simplifying x = 0.053142375Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.613524293, 0.053142375}
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