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Simplifying 3x(x + -4) + 2 = 0 Reorder the terms: 3x(-4 + x) + 2 = 0 (-4 * 3x + x * 3x) + 2 = 0 (-12x + 3x2) + 2 = 0 Reorder the terms: 2 + -12x + 3x2 = 0 Solving 2 + -12x + 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'. 0.6666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -4x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -4x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.6666666667 -4x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -4x + x2 = -0.6666666667 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 = -0.6666666667 + 4 Reorder the terms: 4 + -4x + x2 = -0.6666666667 + 4 Combine like terms: -0.6666666667 + 4 = 3.3333333333 4 + -4x + x2 = 3.3333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.3333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (x + -2) equal to 1.825741858 and -1.825741858.Subproblem 1
x + -2 = 1.825741858 Simplifying x + -2 = 1.825741858 Reorder the terms: -2 + x = 1.825741858 Solving -2 + x = 1.825741858 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 = 1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.825741858 + 2 x = 1.825741858 + 2 Combine like terms: 1.825741858 + 2 = 3.825741858 x = 3.825741858 Simplifying x = 3.825741858Subproblem 2
x + -2 = -1.825741858 Simplifying x + -2 = -1.825741858 Reorder the terms: -2 + x = -1.825741858 Solving -2 + x = -1.825741858 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 = -1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.825741858 + 2 x = -1.825741858 + 2 Combine like terms: -1.825741858 + 2 = 0.174258142 x = 0.174258142 Simplifying x = 0.174258142Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.825741858, 0.174258142}
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