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Simplifying 3x2 + 3x + -23 = 0 Reorder the terms: -23 + 3x + 3x2 = 0 Solving -23 + 3x + 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 + x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + x + x2 = 0 + 7.666666667 x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 x + x2 = 7.666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 7.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 7.666666667 + 0.25 Combine like terms: 7.666666667 + 0.25 = 7.916666667 1.25 + x2 = 7.916666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.916666667 Calculate the square root of the right side: 2.813657169 Break this problem into two subproblems by setting (x + 0.5) equal to 2.813657169 and -2.813657169.Subproblem 1
x + 0.5 = 2.813657169 Simplifying x + 0.5 = 2.813657169 Reorder the terms: 0.5 + x = 2.813657169 Solving 0.5 + x = 2.813657169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.813657169 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.813657169 + -0.5 x = 2.813657169 + -0.5 Combine like terms: 2.813657169 + -0.5 = 2.313657169 x = 2.313657169 Simplifying x = 2.313657169Subproblem 2
x + 0.5 = -2.813657169 Simplifying x + 0.5 = -2.813657169 Reorder the terms: 0.5 + x = -2.813657169 Solving 0.5 + x = -2.813657169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.813657169 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.813657169 + -0.5 x = -2.813657169 + -0.5 Combine like terms: -2.813657169 + -0.5 = -3.313657169 x = -3.313657169 Simplifying x = -3.313657169Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.313657169, -3.313657169}
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