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Simplifying 18x2 + 48x + -17 = 0 Reorder the terms: -17 + 48x + 18x2 = 0 Solving -17 + 48x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.9444444444 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '0.9444444444' to each side of the equation. -0.9444444444 + 2.666666667x + 0.9444444444 + x2 = 0 + 0.9444444444 Reorder the terms: -0.9444444444 + 0.9444444444 + 2.666666667x + x2 = 0 + 0.9444444444 Combine like terms: -0.9444444444 + 0.9444444444 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + 0.9444444444 2.666666667x + x2 = 0 + 0.9444444444 Combine like terms: 0 + 0.9444444444 = 0.9444444444 2.666666667x + x2 = 0.9444444444 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 = 0.9444444444 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 0.9444444444 + 1.777777780 Combine like terms: 0.9444444444 + 1.777777780 = 2.7222222244 1.777777780 + 2.666666667x + x2 = 2.7222222244 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.7222222244 Calculate the square root of the right side: 1.649915823 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.649915823 and -1.649915823.Subproblem 1
x + 1.333333334 = 1.649915823 Simplifying x + 1.333333334 = 1.649915823 Reorder the terms: 1.333333334 + x = 1.649915823 Solving 1.333333334 + x = 1.649915823 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 = 1.649915823 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.649915823 + -1.333333334 x = 1.649915823 + -1.333333334 Combine like terms: 1.649915823 + -1.333333334 = 0.316582489 x = 0.316582489 Simplifying x = 0.316582489Subproblem 2
x + 1.333333334 = -1.649915823 Simplifying x + 1.333333334 = -1.649915823 Reorder the terms: 1.333333334 + x = -1.649915823 Solving 1.333333334 + x = -1.649915823 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 = -1.649915823 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.649915823 + -1.333333334 x = -1.649915823 + -1.333333334 Combine like terms: -1.649915823 + -1.333333334 = -2.983249157 x = -2.983249157 Simplifying x = -2.983249157Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.316582489, -2.983249157}
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