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Simplifying x2 + 8x + 16 = 1.77 Reorder the terms: 16 + 8x + x2 = 1.77 Solving 16 + 8x + x2 = 1.77 Solving for variable 'x'. Reorder the terms: 16 + -1.77 + 8x + x2 = 1.77 + -1.77 Combine like terms: 16 + -1.77 = 14.23 14.23 + 8x + x2 = 1.77 + -1.77 Combine like terms: 1.77 + -1.77 = 0.00 14.23 + 8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-14.23' to each side of the equation. 14.23 + 8x + -14.23 + x2 = 0.00 + -14.23 Reorder the terms: 14.23 + -14.23 + 8x + x2 = 0.00 + -14.23 Combine like terms: 14.23 + -14.23 = 0.00 0.00 + 8x + x2 = 0.00 + -14.23 8x + x2 = 0.00 + -14.23 Combine like terms: 0.00 + -14.23 = -14.23 8x + x2 = -14.23 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 = -14.23 + 16 Reorder the terms: 16 + 8x + x2 = -14.23 + 16 Combine like terms: -14.23 + 16 = 1.77 16 + 8x + x2 = 1.77 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.77 Calculate the square root of the right side: 1.33041347 Break this problem into two subproblems by setting (x + 4) equal to 1.33041347 and -1.33041347.Subproblem 1
x + 4 = 1.33041347 Simplifying x + 4 = 1.33041347 Reorder the terms: 4 + x = 1.33041347 Solving 4 + x = 1.33041347 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 = 1.33041347 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.33041347 + -4 x = 1.33041347 + -4 Combine like terms: 1.33041347 + -4 = -2.66958653 x = -2.66958653 Simplifying x = -2.66958653Subproblem 2
x + 4 = -1.33041347 Simplifying x + 4 = -1.33041347 Reorder the terms: 4 + x = -1.33041347 Solving 4 + x = -1.33041347 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 = -1.33041347 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.33041347 + -4 x = -1.33041347 + -4 Combine like terms: -1.33041347 + -4 = -5.33041347 x = -5.33041347 Simplifying x = -5.33041347Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.66958653, -5.33041347}
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