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Simplifying x2 + 8x + 16 = 2x2 + -14 Reorder the terms: 16 + 8x + x2 = 2x2 + -14 Reorder the terms: 16 + 8x + x2 = -14 + 2x2 Solving 16 + 8x + x2 = -14 + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 14 + 8x + x2 + -2x2 = -14 + 2x2 + 14 + -2x2 Combine like terms: 16 + 14 = 30 30 + 8x + x2 + -2x2 = -14 + 2x2 + 14 + -2x2 Combine like terms: x2 + -2x2 = -1x2 30 + 8x + -1x2 = -14 + 2x2 + 14 + -2x2 Reorder the terms: 30 + 8x + -1x2 = -14 + 14 + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 30 + 8x + -1x2 = 0 + 2x2 + -2x2 30 + 8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -8x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -8x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -8x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -8x + x2 = 0 + 30 -8x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -8x + x2 = 30 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 = 30 + 16 Reorder the terms: 16 + -8x + x2 = 30 + 16 Combine like terms: 30 + 16 = 46 16 + -8x + x2 = 46 Factor a perfect square on the left side: (x + -4)(x + -4) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -4) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -4 = 6.782329983 Simplifying x + -4 = 6.782329983 Reorder the terms: -4 + x = 6.782329983 Solving -4 + x = 6.782329983 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 = 6.782329983 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.782329983 + 4 x = 6.782329983 + 4 Combine like terms: 6.782329983 + 4 = 10.782329983 x = 10.782329983 Simplifying x = 10.782329983Subproblem 2
x + -4 = -6.782329983 Simplifying x + -4 = -6.782329983 Reorder the terms: -4 + x = -6.782329983 Solving -4 + x = -6.782329983 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 = -6.782329983 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.782329983 + 4 x = -6.782329983 + 4 Combine like terms: -6.782329983 + 4 = -2.782329983 x = -2.782329983 Simplifying x = -2.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.782329983, -2.782329983}
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