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Simplifying x2 + -8x + -16 = 23 Reorder the terms: -16 + -8x + x2 = 23 Solving -16 + -8x + x2 = 23 Solving for variable 'x'. Reorder the terms: -16 + -23 + -8x + x2 = 23 + -23 Combine like terms: -16 + -23 = -39 -39 + -8x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -39 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -8x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -8x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -8x + x2 = 0 + 39 -8x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -8x + x2 = 39 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 39 + 16 Reorder the terms: 16 + -8x + x2 = 39 + 16 Combine like terms: 39 + 16 = 55 16 + -8x + x2 = 55 Factor a perfect square on the left side: (x + -4)(x + -4) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -4) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -4 = 7.416198487 Simplifying x + -4 = 7.416198487 Reorder the terms: -4 + x = 7.416198487 Solving -4 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.416198487 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.416198487 + 4 x = 7.416198487 + 4 Combine like terms: 7.416198487 + 4 = 11.416198487 x = 11.416198487 Simplifying x = 11.416198487Subproblem 2
x + -4 = -7.416198487 Simplifying x + -4 = -7.416198487 Reorder the terms: -4 + x = -7.416198487 Solving -4 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.416198487 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.416198487 + 4 x = -7.416198487 + 4 Combine like terms: -7.416198487 + 4 = -3.416198487 x = -3.416198487 Simplifying x = -3.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.416198487, -3.416198487}
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