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Simplifying (x + -5)(6 + x) = x + -6x + 20 Reorder the terms: (-5 + x)(6 + x) = x + -6x + 20 Multiply (-5 + x) * (6 + x) (-5(6 + x) + x(6 + x)) = x + -6x + 20 ((6 * -5 + x * -5) + x(6 + x)) = x + -6x + 20 ((-30 + -5x) + x(6 + x)) = x + -6x + 20 (-30 + -5x + (6 * x + x * x)) = x + -6x + 20 (-30 + -5x + (6x + x2)) = x + -6x + 20 Combine like terms: -5x + 6x = 1x (-30 + 1x + x2) = x + -6x + 20 Reorder the terms: -30 + 1x + x2 = 20 + x + -6x Combine like terms: x + -6x = -5x -30 + 1x + x2 = 20 + -5x Solving -30 + 1x + x2 = 20 + -5x Solving for variable 'x'. Reorder the terms: -30 + -20 + 1x + 5x + x2 = 20 + -5x + -20 + 5x Combine like terms: -30 + -20 = -50 -50 + 1x + 5x + x2 = 20 + -5x + -20 + 5x Combine like terms: 1x + 5x = 6x -50 + 6x + x2 = 20 + -5x + -20 + 5x Reorder the terms: -50 + 6x + x2 = 20 + -20 + -5x + 5x Combine like terms: 20 + -20 = 0 -50 + 6x + x2 = 0 + -5x + 5x -50 + 6x + x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -50 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 6x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 6x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 6x + x2 = 0 + 50 6x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 6x + x2 = 50 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 = 50 + 9 Reorder the terms: 9 + 6x + x2 = 50 + 9 Combine like terms: 50 + 9 = 59 9 + 6x + x2 = 59 Factor a perfect square on the left side: (x + 3)(x + 3) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 3) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 3 = 7.681145748 Simplifying x + 3 = 7.681145748 Reorder the terms: 3 + x = 7.681145748 Solving 3 + x = 7.681145748 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 = 7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.681145748 + -3 x = 7.681145748 + -3 Combine like terms: 7.681145748 + -3 = 4.681145748 x = 4.681145748 Simplifying x = 4.681145748Subproblem 2
x + 3 = -7.681145748 Simplifying x + 3 = -7.681145748 Reorder the terms: 3 + x = -7.681145748 Solving 3 + x = -7.681145748 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 = -7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.681145748 + -3 x = -7.681145748 + -3 Combine like terms: -7.681145748 + -3 = -10.681145748 x = -10.681145748 Simplifying x = -10.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.681145748, -10.681145748}
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