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Simplifying (2x + 23) = (x2 + -8) Reorder the terms: (23 + 2x) = (x2 + -8) Remove parenthesis around (23 + 2x) 23 + 2x = (x2 + -8) Reorder the terms: 23 + 2x = (-8 + x2) Remove parenthesis around (-8 + x2) 23 + 2x = -8 + x2 Solving 23 + 2x = -8 + x2 Solving for variable 'x'. Reorder the terms: 23 + 8 + 2x + -1x2 = -8 + x2 + 8 + -1x2 Combine like terms: 23 + 8 = 31 31 + 2x + -1x2 = -8 + x2 + 8 + -1x2 Reorder the terms: 31 + 2x + -1x2 = -8 + 8 + x2 + -1x2 Combine like terms: -8 + 8 = 0 31 + 2x + -1x2 = 0 + x2 + -1x2 31 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 31 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + -2x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -2x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -2x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -2x + x2 = 0 + 31 -2x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -2x + x2 = 31 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 = 31 + 1 Reorder the terms: 1 + -2x + x2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + -2x + x2 = 32 Factor a perfect square on the left side: (x + -1)(x + -1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -1) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -1 = 5.656854249 Simplifying x + -1 = 5.656854249 Reorder the terms: -1 + x = 5.656854249 Solving -1 + x = 5.656854249 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 = 5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.656854249 + 1 x = 5.656854249 + 1 Combine like terms: 5.656854249 + 1 = 6.656854249 x = 6.656854249 Simplifying x = 6.656854249Subproblem 2
x + -1 = -5.656854249 Simplifying x + -1 = -5.656854249 Reorder the terms: -1 + x = -5.656854249 Solving -1 + x = -5.656854249 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 = -5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.656854249 + 1 x = -5.656854249 + 1 Combine like terms: -5.656854249 + 1 = -4.656854249 x = -4.656854249 Simplifying x = -4.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.656854249, -4.656854249}
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