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Simplifying 5x + -4 = 3x2 + -18x Reorder the terms: -4 + 5x = 3x2 + -18x Reorder the terms: -4 + 5x = -18x + 3x2 Solving -4 + 5x = -18x + 3x2 Solving for variable 'x'. Combine like terms: 5x + 18x = 23x -4 + 23x + -3x2 = -18x + 3x2 + 18x + -3x2 Reorder the terms: -4 + 23x + -3x2 = -18x + 18x + 3x2 + -3x2 Combine like terms: -18x + 18x = 0 -4 + 23x + -3x2 = 0 + 3x2 + -3x2 -4 + 23x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -4 + 23x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -7.666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -7.666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + -1.333333333 -7.666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -7.666666667x + x2 = -1.333333333 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -1.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -1.333333333 + 14.69444445 Combine like terms: -1.333333333 + 14.69444445 = 13.361111117 14.69444445 + -7.666666667x + x2 = 13.361111117 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 13.361111117 Calculate the square root of the right side: 3.655285367 Break this problem into two subproblems by setting (x + -3.833333334) equal to 3.655285367 and -3.655285367.Subproblem 1
x + -3.833333334 = 3.655285367 Simplifying x + -3.833333334 = 3.655285367 Reorder the terms: -3.833333334 + x = 3.655285367 Solving -3.833333334 + x = 3.655285367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 3.655285367 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 3.655285367 + 3.833333334 x = 3.655285367 + 3.833333334 Combine like terms: 3.655285367 + 3.833333334 = 7.488618701 x = 7.488618701 Simplifying x = 7.488618701Subproblem 2
x + -3.833333334 = -3.655285367 Simplifying x + -3.833333334 = -3.655285367 Reorder the terms: -3.833333334 + x = -3.655285367 Solving -3.833333334 + x = -3.655285367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -3.655285367 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -3.655285367 + 3.833333334 x = -3.655285367 + 3.833333334 Combine like terms: -3.655285367 + 3.833333334 = 0.178047967 x = 0.178047967 Simplifying x = 0.178047967Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.488618701, 0.178047967}
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