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Simplifying 18x2 = 48x + -3 Reorder the terms: 18x2 = -3 + 48x Solving 18x2 = -3 + 48x Solving for variable 'x'. Reorder the terms: 3 + -48x + 18x2 = -3 + 48x + 3 + -48x Reorder the terms: 3 + -48x + 18x2 = -3 + 3 + 48x + -48x Combine like terms: -3 + 3 = 0 3 + -48x + 18x2 = 0 + 48x + -48x 3 + -48x + 18x2 = 48x + -48x Combine like terms: 48x + -48x = 0 3 + -48x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -16x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -16x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + -16x + 6x2 = 0 Solving 1 + -16x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -2.666666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -2.666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + -0.1666666667 -2.666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -2.666666667x + x2 = -0.1666666667 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 = -0.1666666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -0.1666666667 + 1.777777780 Combine like terms: -0.1666666667 + 1.777777780 = 1.6111111133 1.777777780 + -2.666666667x + x2 = 1.6111111133 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.6111111133 Calculate the square root of the right side: 1.269295519 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.269295519 and -1.269295519.Subproblem 1
x + -1.333333334 = 1.269295519 Simplifying x + -1.333333334 = 1.269295519 Reorder the terms: -1.333333334 + x = 1.269295519 Solving -1.333333334 + x = 1.269295519 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 = 1.269295519 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.269295519 + 1.333333334 x = 1.269295519 + 1.333333334 Combine like terms: 1.269295519 + 1.333333334 = 2.602628853 x = 2.602628853 Simplifying x = 2.602628853Subproblem 2
x + -1.333333334 = -1.269295519 Simplifying x + -1.333333334 = -1.269295519 Reorder the terms: -1.333333334 + x = -1.269295519 Solving -1.333333334 + x = -1.269295519 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 = -1.269295519 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.269295519 + 1.333333334 x = -1.269295519 + 1.333333334 Combine like terms: -1.269295519 + 1.333333334 = 0.064037815 x = 0.064037815 Simplifying x = 0.064037815Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.602628853, 0.064037815}Solution
x = {2.602628853, 0.064037815}
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