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Simplifying 3x2 + 23x + -500 = 0 Reorder the terms: -500 + 23x + 3x2 = 0 Solving -500 + 23x + 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'. -166.6666667 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + 7.666666667x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + 7.666666667x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + 7.666666667x + x2 = 0 + 166.6666667 7.666666667x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 7.666666667x + x2 = 166.6666667 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 = 166.6666667 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 166.6666667 + 14.69444445 Combine like terms: 166.6666667 + 14.69444445 = 181.36111115 14.69444445 + 7.666666667x + x2 = 181.36111115 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 181.36111115 Calculate the square root of the right side: 13.46703795 Break this problem into two subproblems by setting (x + 3.833333334) equal to 13.46703795 and -13.46703795.Subproblem 1
x + 3.833333334 = 13.46703795 Simplifying x + 3.833333334 = 13.46703795 Reorder the terms: 3.833333334 + x = 13.46703795 Solving 3.833333334 + x = 13.46703795 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 = 13.46703795 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 13.46703795 + -3.833333334 x = 13.46703795 + -3.833333334 Combine like terms: 13.46703795 + -3.833333334 = 9.633704616 x = 9.633704616 Simplifying x = 9.633704616Subproblem 2
x + 3.833333334 = -13.46703795 Simplifying x + 3.833333334 = -13.46703795 Reorder the terms: 3.833333334 + x = -13.46703795 Solving 3.833333334 + x = -13.46703795 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 = -13.46703795 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -13.46703795 + -3.833333334 x = -13.46703795 + -3.833333334 Combine like terms: -13.46703795 + -3.833333334 = -17.300371284 x = -17.300371284 Simplifying x = -17.300371284Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.633704616, -17.300371284}
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