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Simplifying 0 = 3x2 + -6x + -23 Reorder the terms: 0 = -23 + -6x + 3x2 Solving 0 = -23 + -6x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 23 = 23 23 + 6x + -3x2 = -23 + -6x + 3x2 + 23 + 6x + -3x2 Reorder the terms: 23 + 6x + -3x2 = -23 + 23 + -6x + 6x + 3x2 + -3x2 Combine like terms: -23 + 23 = 0 23 + 6x + -3x2 = 0 + -6x + 6x + 3x2 + -3x2 23 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 23 + 6x + -3x2 = 0 + 3x2 + -3x2 23 + 6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 23 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + -2x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + -2x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 7.666666667 -2x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 -2x + x2 = 7.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 7.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 7.666666667 + 1 Combine like terms: 7.666666667 + 1 = 8.666666667 1 + -2x + x2 = 8.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 8.666666667 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (x + -1) equal to 2.943920289 and -2.943920289.Subproblem 1
x + -1 = 2.943920289 Simplifying x + -1 = 2.943920289 Reorder the terms: -1 + x = 2.943920289 Solving -1 + x = 2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.943920289 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.943920289 + 1 x = 2.943920289 + 1 Combine like terms: 2.943920289 + 1 = 3.943920289 x = 3.943920289 Simplifying x = 3.943920289Subproblem 2
x + -1 = -2.943920289 Simplifying x + -1 = -2.943920289 Reorder the terms: -1 + x = -2.943920289 Solving -1 + x = -2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.943920289 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.943920289 + 1 x = -2.943920289 + 1 Combine like terms: -2.943920289 + 1 = -1.943920289 x = -1.943920289 Simplifying x = -1.943920289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.943920289, -1.943920289}
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