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Simplifying (3x + -6)(x + 0.33) = 0 Reorder the terms: (-6 + 3x)(x + 0.33) = 0 Reorder the terms: (-6 + 3x)(0.33 + x) = 0 Multiply (-6 + 3x) * (0.33 + x) (-6(0.33 + x) + 3x * (0.33 + x)) = 0 ((0.33 * -6 + x * -6) + 3x * (0.33 + x)) = 0 ((-1.98 + -6x) + 3x * (0.33 + x)) = 0 (-1.98 + -6x + (0.33 * 3x + x * 3x)) = 0 (-1.98 + -6x + (0.99x + 3x2)) = 0 Combine like terms: -6x + 0.99x = -5.01x (-1.98 + -5.01x + 3x2) = 0 Solving -1.98 + -5.01x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.66 + -1.67x + x2 = 0 Move the constant term to the right: Add '0.66' to each side of the equation. -0.66 + -1.67x + 0.66 + x2 = 0 + 0.66 Reorder the terms: -0.66 + 0.66 + -1.67x + x2 = 0 + 0.66 Combine like terms: -0.66 + 0.66 = 0.00 0.00 + -1.67x + x2 = 0 + 0.66 -1.67x + x2 = 0 + 0.66 Combine like terms: 0 + 0.66 = 0.66 -1.67x + x2 = 0.66 The x term is -1.67x. Take half its coefficient (-0.835). Square it (0.697225) and add it to both sides. Add '0.697225' to each side of the equation. -1.67x + 0.697225 + x2 = 0.66 + 0.697225 Reorder the terms: 0.697225 + -1.67x + x2 = 0.66 + 0.697225 Combine like terms: 0.66 + 0.697225 = 1.357225 0.697225 + -1.67x + x2 = 1.357225 Factor a perfect square on the left side: (x + -0.835)(x + -0.835) = 1.357225 Calculate the square root of the right side: 1.165 Break this problem into two subproblems by setting (x + -0.835) equal to 1.165 and -1.165.Subproblem 1
x + -0.835 = 1.165 Simplifying x + -0.835 = 1.165 Reorder the terms: -0.835 + x = 1.165 Solving -0.835 + x = 1.165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.835' to each side of the equation. -0.835 + 0.835 + x = 1.165 + 0.835 Combine like terms: -0.835 + 0.835 = 0.000 0.000 + x = 1.165 + 0.835 x = 1.165 + 0.835 Combine like terms: 1.165 + 0.835 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.835 = -1.165 Simplifying x + -0.835 = -1.165 Reorder the terms: -0.835 + x = -1.165 Solving -0.835 + x = -1.165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.835' to each side of the equation. -0.835 + 0.835 + x = -1.165 + 0.835 Combine like terms: -0.835 + 0.835 = 0.000 0.000 + x = -1.165 + 0.835 x = -1.165 + 0.835 Combine like terms: -1.165 + 0.835 = -0.33 x = -0.33 Simplifying x = -0.33Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.33}
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