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Simplifying 3x2 + -20x + -384 = 0 Reorder the terms: -384 + -20x + 3x2 = 0 Solving -384 + -20x + 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'. -128 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + -6.666666667x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -6.666666667x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -6.666666667x + x2 = 0 + 128 -6.666666667x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -6.666666667x + x2 = 128 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = 128 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 128 + 11.11111112 Combine like terms: 128 + 11.11111112 = 139.11111112 11.11111112 + -6.666666667x + x2 = 139.11111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 139.11111112 Calculate the square root of the right side: 11.794537342 Break this problem into two subproblems by setting (x + -3.333333334) equal to 11.794537342 and -11.794537342.Subproblem 1
x + -3.333333334 = 11.794537342 Simplifying x + -3.333333334 = 11.794537342 Reorder the terms: -3.333333334 + x = 11.794537342 Solving -3.333333334 + x = 11.794537342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 11.794537342 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 11.794537342 + 3.333333334 x = 11.794537342 + 3.333333334 Combine like terms: 11.794537342 + 3.333333334 = 15.127870676 x = 15.127870676 Simplifying x = 15.127870676Subproblem 2
x + -3.333333334 = -11.794537342 Simplifying x + -3.333333334 = -11.794537342 Reorder the terms: -3.333333334 + x = -11.794537342 Solving -3.333333334 + x = -11.794537342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -11.794537342 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -11.794537342 + 3.333333334 x = -11.794537342 + 3.333333334 Combine like terms: -11.794537342 + 3.333333334 = -8.461204008 x = -8.461204008 Simplifying x = -8.461204008Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.127870676, -8.461204008}
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