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Simplifying 48 = (x + -2)(x + 8) Reorder the terms: 48 = (-2 + x)(x + 8) Reorder the terms: 48 = (-2 + x)(8 + x) Multiply (-2 + x) * (8 + x) 48 = (-2(8 + x) + x(8 + x)) 48 = ((8 * -2 + x * -2) + x(8 + x)) 48 = ((-16 + -2x) + x(8 + x)) 48 = (-16 + -2x + (8 * x + x * x)) 48 = (-16 + -2x + (8x + x2)) Combine like terms: -2x + 8x = 6x 48 = (-16 + 6x + x2) Solving 48 = -16 + 6x + x2 Solving for variable 'x'. Combine like terms: 48 + 16 = 64 64 + -6x + -1x2 = -16 + 6x + x2 + 16 + -6x + -1x2 Reorder the terms: 64 + -6x + -1x2 = -16 + 16 + 6x + -6x + x2 + -1x2 Combine like terms: -16 + 16 = 0 64 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 64 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 64 + -6x + -1x2 = 0 + x2 + -1x2 64 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 64 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 6x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 6x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 6x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 6x + x2 = 0 + 64 6x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 6x + x2 = 64 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 64 + 9 Reorder the terms: 9 + 6x + x2 = 64 + 9 Combine like terms: 64 + 9 = 73 9 + 6x + x2 = 73 Factor a perfect square on the left side: (x + 3)(x + 3) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 3) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 3 = 8.544003745 Simplifying x + 3 = 8.544003745 Reorder the terms: 3 + x = 8.544003745 Solving 3 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.544003745 + -3 x = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 x = 5.544003745 Simplifying x = 5.544003745Subproblem 2
x + 3 = -8.544003745 Simplifying x + 3 = -8.544003745 Reorder the terms: 3 + x = -8.544003745 Solving 3 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.544003745 + -3 x = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 x = -11.544003745 Simplifying x = -11.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.544003745, -11.544003745}
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