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Simplifying 2x2 + -16x + 64 = 39 Reorder the terms: 64 + -16x + 2x2 = 39 Solving 64 + -16x + 2x2 = 39 Solving for variable 'x'. Reorder the terms: 64 + -39 + -16x + 2x2 = 39 + -39 Combine like terms: 64 + -39 = 25 25 + -16x + 2x2 = 39 + -39 Combine like terms: 39 + -39 = 0 25 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -8x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -8x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -8x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -8x + x2 = 0 + -12.5 -8x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -8x + x2 = -12.5 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 = -12.5 + 16 Reorder the terms: 16 + -8x + x2 = -12.5 + 16 Combine like terms: -12.5 + 16 = 3.5 16 + -8x + x2 = 3.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -4) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -4 = 1.870828693 Simplifying x + -4 = 1.870828693 Reorder the terms: -4 + x = 1.870828693 Solving -4 + x = 1.870828693 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 = 1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.870828693 + 4 x = 1.870828693 + 4 Combine like terms: 1.870828693 + 4 = 5.870828693 x = 5.870828693 Simplifying x = 5.870828693Subproblem 2
x + -4 = -1.870828693 Simplifying x + -4 = -1.870828693 Reorder the terms: -4 + x = -1.870828693 Solving -4 + x = -1.870828693 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 = -1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.870828693 + 4 x = -1.870828693 + 4 Combine like terms: -1.870828693 + 4 = 2.129171307 x = 2.129171307 Simplifying x = 2.129171307Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.870828693, 2.129171307}
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