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Simplifying 8x + 8 = x2 + -5 Reorder the terms: 8 + 8x = x2 + -5 Reorder the terms: 8 + 8x = -5 + x2 Solving 8 + 8x = -5 + x2 Solving for variable 'x'. Reorder the terms: 8 + 5 + 8x + -1x2 = -5 + x2 + 5 + -1x2 Combine like terms: 8 + 5 = 13 13 + 8x + -1x2 = -5 + x2 + 5 + -1x2 Reorder the terms: 13 + 8x + -1x2 = -5 + 5 + x2 + -1x2 Combine like terms: -5 + 5 = 0 13 + 8x + -1x2 = 0 + x2 + -1x2 13 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -8x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -8x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -8x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8x + x2 = 0 + 13 -8x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -8x + x2 = 13 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 = 13 + 16 Reorder the terms: 16 + -8x + x2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + -8x + x2 = 29 Factor a perfect square on the left side: (x + -4)(x + -4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -4) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -4 = 5.385164807 Simplifying x + -4 = 5.385164807 Reorder the terms: -4 + x = 5.385164807 Solving -4 + x = 5.385164807 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 = 5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.385164807 + 4 x = 5.385164807 + 4 Combine like terms: 5.385164807 + 4 = 9.385164807 x = 9.385164807 Simplifying x = 9.385164807Subproblem 2
x + -4 = -5.385164807 Simplifying x + -4 = -5.385164807 Reorder the terms: -4 + x = -5.385164807 Solving -4 + x = -5.385164807 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 = -5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.385164807 + 4 x = -5.385164807 + 4 Combine like terms: -5.385164807 + 4 = -1.385164807 x = -1.385164807 Simplifying x = -1.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.385164807, -1.385164807}
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