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Simplifying x2 + 2x + 8 = 54 Reorder the terms: 8 + 2x + x2 = 54 Solving 8 + 2x + x2 = 54 Solving for variable 'x'. Reorder the terms: 8 + -54 + 2x + x2 = 54 + -54 Combine like terms: 8 + -54 = -46 -46 + 2x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -46 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 2x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 2x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 2x + x2 = 0 + 46 2x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 2x + x2 = 46 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 = 46 + 1 Reorder the terms: 1 + 2x + x2 = 46 + 1 Combine like terms: 46 + 1 = 47 1 + 2x + x2 = 47 Factor a perfect square on the left side: (x + 1)(x + 1) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 1) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 1 = 6.8556546 Simplifying x + 1 = 6.8556546 Reorder the terms: 1 + x = 6.8556546 Solving 1 + x = 6.8556546 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 = 6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.8556546 + -1 x = 6.8556546 + -1 Combine like terms: 6.8556546 + -1 = 5.8556546 x = 5.8556546 Simplifying x = 5.8556546Subproblem 2
x + 1 = -6.8556546 Simplifying x + 1 = -6.8556546 Reorder the terms: 1 + x = -6.8556546 Solving 1 + x = -6.8556546 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 = -6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.8556546 + -1 x = -6.8556546 + -1 Combine like terms: -6.8556546 + -1 = -7.8556546 x = -7.8556546 Simplifying x = -7.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.8556546, -7.8556546}
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