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Simplifying (x + -3)(x + 11) = 31 Reorder the terms: (-3 + x)(x + 11) = 31 Reorder the terms: (-3 + x)(11 + x) = 31 Multiply (-3 + x) * (11 + x) (-3(11 + x) + x(11 + x)) = 31 ((11 * -3 + x * -3) + x(11 + x)) = 31 ((-33 + -3x) + x(11 + x)) = 31 (-33 + -3x + (11 * x + x * x)) = 31 (-33 + -3x + (11x + x2)) = 31 Combine like terms: -3x + 11x = 8x (-33 + 8x + x2) = 31 Solving -33 + 8x + x2 = 31 Solving for variable 'x'. Reorder the terms: -33 + -31 + 8x + x2 = 31 + -31 Combine like terms: -33 + -31 = -64 -64 + 8x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -64 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 8x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 8x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 8x + x2 = 0 + 64 8x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 8x + x2 = 64 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 = 64 + 16 Reorder the terms: 16 + 8x + x2 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + 8x + x2 = 80 Factor a perfect square on the left side: (x + 4)(x + 4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 4) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 4 = 8.94427191 Simplifying x + 4 = 8.94427191 Reorder the terms: 4 + x = 8.94427191 Solving 4 + x = 8.94427191 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 = 8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.94427191 + -4 x = 8.94427191 + -4 Combine like terms: 8.94427191 + -4 = 4.94427191 x = 4.94427191 Simplifying x = 4.94427191Subproblem 2
x + 4 = -8.94427191 Simplifying x + 4 = -8.94427191 Reorder the terms: 4 + x = -8.94427191 Solving 4 + x = -8.94427191 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 = -8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.94427191 + -4 x = -8.94427191 + -4 Combine like terms: -8.94427191 + -4 = -12.94427191 x = -12.94427191 Simplifying x = -12.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.94427191, -12.94427191}
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