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Simplifying -3x2 + -23x + 30 = 0 Reorder the terms: 30 + -23x + -3x2 = 0 Solving 30 + -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'. -10 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 7.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 7.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7.666666667x + x2 = 0 + 10 7.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 7.666666667x + x2 = 10 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 = 10 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 10 + 14.69444445 Combine like terms: 10 + 14.69444445 = 24.69444445 14.69444445 + 7.666666667x + x2 = 24.69444445 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 24.69444445 Calculate the square root of the right side: 4.969350506 Break this problem into two subproblems by setting (x + 3.833333334) equal to 4.969350506 and -4.969350506.Subproblem 1
x + 3.833333334 = 4.969350506 Simplifying x + 3.833333334 = 4.969350506 Reorder the terms: 3.833333334 + x = 4.969350506 Solving 3.833333334 + x = 4.969350506 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 = 4.969350506 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 4.969350506 + -3.833333334 x = 4.969350506 + -3.833333334 Combine like terms: 4.969350506 + -3.833333334 = 1.136017172 x = 1.136017172 Simplifying x = 1.136017172Subproblem 2
x + 3.833333334 = -4.969350506 Simplifying x + 3.833333334 = -4.969350506 Reorder the terms: 3.833333334 + x = -4.969350506 Solving 3.833333334 + x = -4.969350506 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 = -4.969350506 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -4.969350506 + -3.833333334 x = -4.969350506 + -3.833333334 Combine like terms: -4.969350506 + -3.833333334 = -8.80268384 x = -8.80268384 Simplifying x = -8.80268384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.136017172, -8.80268384}
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