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Simplifying x2 + 8x + -64 = 3 Reorder the terms: -64 + 8x + x2 = 3 Solving -64 + 8x + x2 = 3 Solving for variable 'x'. Reorder the terms: -64 + -3 + 8x + x2 = 3 + -3 Combine like terms: -64 + -3 = -67 -67 + 8x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -67 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 8x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + 8x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 8x + x2 = 0 + 67 8x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 8x + x2 = 67 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 = 67 + 16 Reorder the terms: 16 + 8x + x2 = 67 + 16 Combine like terms: 67 + 16 = 83 16 + 8x + x2 = 83 Factor a perfect square on the left side: (x + 4)(x + 4) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + 4) equal to 9.110433579 and -9.110433579.Subproblem 1
x + 4 = 9.110433579 Simplifying x + 4 = 9.110433579 Reorder the terms: 4 + x = 9.110433579 Solving 4 + x = 9.110433579 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 = 9.110433579 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.110433579 + -4 x = 9.110433579 + -4 Combine like terms: 9.110433579 + -4 = 5.110433579 x = 5.110433579 Simplifying x = 5.110433579Subproblem 2
x + 4 = -9.110433579 Simplifying x + 4 = -9.110433579 Reorder the terms: 4 + x = -9.110433579 Solving 4 + x = -9.110433579 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 = -9.110433579 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.110433579 + -4 x = -9.110433579 + -4 Combine like terms: -9.110433579 + -4 = -13.110433579 x = -13.110433579 Simplifying x = -13.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.110433579, -13.110433579}
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