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Simplifying 3x2 + 24x + 23 = 0 Reorder the terms: 23 + 24x + 3x2 = 0 Solving 23 + 24x + 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'. 7.666666667 + 8x + x2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + 8x + -7.666666667 + x2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + 8x + x2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + 8x + x2 = 0 + -7.666666667 8x + x2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 8x + x2 = -7.666666667 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -7.666666667 + 16 Reorder the terms: 16 + 8x + x2 = -7.666666667 + 16 Combine like terms: -7.666666667 + 16 = 8.333333333 16 + 8x + x2 = 8.333333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 8.333333333 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (x + 4) equal to 2.886751346 and -2.886751346.Subproblem 1
x + 4 = 2.886751346 Simplifying x + 4 = 2.886751346 Reorder the terms: 4 + x = 2.886751346 Solving 4 + x = 2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.886751346 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.886751346 + -4 x = 2.886751346 + -4 Combine like terms: 2.886751346 + -4 = -1.113248654 x = -1.113248654 Simplifying x = -1.113248654Subproblem 2
x + 4 = -2.886751346 Simplifying x + 4 = -2.886751346 Reorder the terms: 4 + x = -2.886751346 Solving 4 + x = -2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.886751346 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.886751346 + -4 x = -2.886751346 + -4 Combine like terms: -2.886751346 + -4 = -6.886751346 x = -6.886751346 Simplifying x = -6.886751346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.113248654, -6.886751346}
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