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Simplifying x2 + 8x + 16 = 2.67 Reorder the terms: 16 + 8x + x2 = 2.67 Solving 16 + 8x + x2 = 2.67 Solving for variable 'x'. Reorder the terms: 16 + -2.67 + 8x + x2 = 2.67 + -2.67 Combine like terms: 16 + -2.67 = 13.33 13.33 + 8x + x2 = 2.67 + -2.67 Combine like terms: 2.67 + -2.67 = 0.00 13.33 + 8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-13.33' to each side of the equation. 13.33 + 8x + -13.33 + x2 = 0.00 + -13.33 Reorder the terms: 13.33 + -13.33 + 8x + x2 = 0.00 + -13.33 Combine like terms: 13.33 + -13.33 = 0.00 0.00 + 8x + x2 = 0.00 + -13.33 8x + x2 = 0.00 + -13.33 Combine like terms: 0.00 + -13.33 = -13.33 8x + x2 = -13.33 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 = -13.33 + 16 Reorder the terms: 16 + 8x + x2 = -13.33 + 16 Combine like terms: -13.33 + 16 = 2.67 16 + 8x + x2 = 2.67 Factor a perfect square on the left side: (x + 4)(x + 4) = 2.67 Calculate the square root of the right side: 1.634013464 Break this problem into two subproblems by setting (x + 4) equal to 1.634013464 and -1.634013464.Subproblem 1
x + 4 = 1.634013464 Simplifying x + 4 = 1.634013464 Reorder the terms: 4 + x = 1.634013464 Solving 4 + x = 1.634013464 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 = 1.634013464 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.634013464 + -4 x = 1.634013464 + -4 Combine like terms: 1.634013464 + -4 = -2.365986536 x = -2.365986536 Simplifying x = -2.365986536Subproblem 2
x + 4 = -1.634013464 Simplifying x + 4 = -1.634013464 Reorder the terms: 4 + x = -1.634013464 Solving 4 + x = -1.634013464 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 = -1.634013464 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.634013464 + -4 x = -1.634013464 + -4 Combine like terms: -1.634013464 + -4 = -5.634013464 x = -5.634013464 Simplifying x = -5.634013464Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.365986536, -5.634013464}
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