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Simplifying x2 + 8x + 8 = 2x2 + -2x + -40 Reorder the terms: 8 + 8x + x2 = 2x2 + -2x + -40 Reorder the terms: 8 + 8x + x2 = -40 + -2x + 2x2 Solving 8 + 8x + x2 = -40 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: 8 + 40 + 8x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: 8 + 40 = 48 48 + 8x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: 8x + 2x = 10x 48 + 10x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 48 + 10x + -1x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Reorder the terms: 48 + 10x + -1x2 = -40 + 40 + -2x + 2x + 2x2 + -2x2 Combine like terms: -40 + 40 = 0 48 + 10x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2 48 + 10x + -1x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 48 + 10x + -1x2 = 0 + 2x2 + -2x2 48 + 10x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 48 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + -10x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -10x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -10x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -10x + x2 = 0 + 48 -10x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -10x + x2 = 48 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 48 + 25 Reorder the terms: 25 + -10x + x2 = 48 + 25 Combine like terms: 48 + 25 = 73 25 + -10x + x2 = 73 Factor a perfect square on the left side: (x + -5)(x + -5) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -5) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -5 = 8.544003745 Simplifying x + -5 = 8.544003745 Reorder the terms: -5 + x = 8.544003745 Solving -5 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 8.544003745 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.544003745 + 5 x = 8.544003745 + 5 Combine like terms: 8.544003745 + 5 = 13.544003745 x = 13.544003745 Simplifying x = 13.544003745Subproblem 2
x + -5 = -8.544003745 Simplifying x + -5 = -8.544003745 Reorder the terms: -5 + x = -8.544003745 Solving -5 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -8.544003745 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.544003745 + 5 x = -8.544003745 + 5 Combine like terms: -8.544003745 + 5 = -3.544003745 x = -3.544003745 Simplifying x = -3.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.544003745, -3.544003745}
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