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Simplifying x2 + x2 + -8x + 16 = 49 Reorder the terms: 16 + -8x + x2 + x2 = 49 Combine like terms: x2 + x2 = 2x2 16 + -8x + 2x2 = 49 Solving 16 + -8x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: 16 + -49 + -8x + 2x2 = 49 + -49 Combine like terms: 16 + -49 = -33 -33 + -8x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -33 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -4x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -4x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -4x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -4x + x2 = 0 + 16.5 -4x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -4x + x2 = 16.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 16.5 + 4 Reorder the terms: 4 + -4x + x2 = 16.5 + 4 Combine like terms: 16.5 + 4 = 20.5 4 + -4x + x2 = 20.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + -2) equal to 4.527692569 and -4.527692569.Subproblem 1
x + -2 = 4.527692569 Simplifying x + -2 = 4.527692569 Reorder the terms: -2 + x = 4.527692569 Solving -2 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.527692569 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.527692569 + 2 x = 4.527692569 + 2 Combine like terms: 4.527692569 + 2 = 6.527692569 x = 6.527692569 Simplifying x = 6.527692569Subproblem 2
x + -2 = -4.527692569 Simplifying x + -2 = -4.527692569 Reorder the terms: -2 + x = -4.527692569 Solving -2 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.527692569 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.527692569 + 2 x = -4.527692569 + 2 Combine like terms: -4.527692569 + 2 = -2.527692569 x = -2.527692569 Simplifying x = -2.527692569Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.527692569, -2.527692569}
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