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Simplifying x2 + 8x + 16 = 1.78 Reorder the terms: 16 + 8x + x2 = 1.78 Solving 16 + 8x + x2 = 1.78 Solving for variable 'x'. Reorder the terms: 16 + -1.78 + 8x + x2 = 1.78 + -1.78 Combine like terms: 16 + -1.78 = 14.22 14.22 + 8x + x2 = 1.78 + -1.78 Combine like terms: 1.78 + -1.78 = 0.00 14.22 + 8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-14.22' to each side of the equation. 14.22 + 8x + -14.22 + x2 = 0.00 + -14.22 Reorder the terms: 14.22 + -14.22 + 8x + x2 = 0.00 + -14.22 Combine like terms: 14.22 + -14.22 = 0.00 0.00 + 8x + x2 = 0.00 + -14.22 8x + x2 = 0.00 + -14.22 Combine like terms: 0.00 + -14.22 = -14.22 8x + x2 = -14.22 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 = -14.22 + 16 Reorder the terms: 16 + 8x + x2 = -14.22 + 16 Combine like terms: -14.22 + 16 = 1.78 16 + 8x + x2 = 1.78 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.78 Calculate the square root of the right side: 1.334166406 Break this problem into two subproblems by setting (x + 4) equal to 1.334166406 and -1.334166406.Subproblem 1
x + 4 = 1.334166406 Simplifying x + 4 = 1.334166406 Reorder the terms: 4 + x = 1.334166406 Solving 4 + x = 1.334166406 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 = 1.334166406 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.334166406 + -4 x = 1.334166406 + -4 Combine like terms: 1.334166406 + -4 = -2.665833594 x = -2.665833594 Simplifying x = -2.665833594Subproblem 2
x + 4 = -1.334166406 Simplifying x + 4 = -1.334166406 Reorder the terms: 4 + x = -1.334166406 Solving 4 + x = -1.334166406 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 = -1.334166406 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.334166406 + -4 x = -1.334166406 + -4 Combine like terms: -1.334166406 + -4 = -5.334166406 x = -5.334166406 Simplifying x = -5.334166406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.665833594, -5.334166406}
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