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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 = 23.666666667 16 + 8x + x2 = 23.666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 23.666666667 Calculate the square root of the right side: 4.86483984 Break this problem into two subproblems by setting (x + 4) equal to 4.86483984 and -4.86483984.Subproblem 1
x + 4 = 4.86483984 Simplifying x + 4 = 4.86483984 Reorder the terms: 4 + x = 4.86483984 Solving 4 + x = 4.86483984 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 = 4.86483984 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.86483984 + -4 x = 4.86483984 + -4 Combine like terms: 4.86483984 + -4 = 0.86483984 x = 0.86483984 Simplifying x = 0.86483984Subproblem 2
x + 4 = -4.86483984 Simplifying x + 4 = -4.86483984 Reorder the terms: 4 + x = -4.86483984 Solving 4 + x = -4.86483984 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 = -4.86483984 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.86483984 + -4 x = -4.86483984 + -4 Combine like terms: -4.86483984 + -4 = -8.86483984 x = -8.86483984 Simplifying x = -8.86483984Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.86483984, -8.86483984}
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