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Simplifying 8x2 + 16x + -23 = 0 Reorder the terms: -23 + 16x + 8x2 = 0 Solving -23 + 16x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + 2x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + 2x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + 2x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + 2x + x2 = 0 + 2.875 2x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 2x + x2 = 2.875 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 = 2.875 + 1 Reorder the terms: 1 + 2x + x2 = 2.875 + 1 Combine like terms: 2.875 + 1 = 3.875 1 + 2x + x2 = 3.875 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.875 Calculate the square root of the right side: 1.968501969 Break this problem into two subproblems by setting (x + 1) equal to 1.968501969 and -1.968501969.Subproblem 1
x + 1 = 1.968501969 Simplifying x + 1 = 1.968501969 Reorder the terms: 1 + x = 1.968501969 Solving 1 + x = 1.968501969 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 = 1.968501969 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.968501969 + -1 x = 1.968501969 + -1 Combine like terms: 1.968501969 + -1 = 0.968501969 x = 0.968501969 Simplifying x = 0.968501969Subproblem 2
x + 1 = -1.968501969 Simplifying x + 1 = -1.968501969 Reorder the terms: 1 + x = -1.968501969 Solving 1 + x = -1.968501969 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 = -1.968501969 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.968501969 + -1 x = -1.968501969 + -1 Combine like terms: -1.968501969 + -1 = -2.968501969 x = -2.968501969 Simplifying x = -2.968501969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.968501969, -2.968501969}
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