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Simplifying 1 + 13x + x2 = -5 + -8x Solving 1 + 13x + x2 = -5 + -8x Solving for variable 'x'. Reorder the terms: 1 + 5 + 13x + 8x + x2 = -5 + -8x + 5 + 8x Combine like terms: 1 + 5 = 6 6 + 13x + 8x + x2 = -5 + -8x + 5 + 8x Combine like terms: 13x + 8x = 21x 6 + 21x + x2 = -5 + -8x + 5 + 8x Reorder the terms: 6 + 21x + x2 = -5 + 5 + -8x + 8x Combine like terms: -5 + 5 = 0 6 + 21x + x2 = 0 + -8x + 8x 6 + 21x + x2 = -8x + 8x Combine like terms: -8x + 8x = 0 6 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 21x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 21x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 21x + x2 = 0 + -6 21x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 21x + x2 = -6 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -6 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -6 + 110.25 Combine like terms: -6 + 110.25 = 104.25 110.25 + 21x + x2 = 104.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + 10.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + 10.5 = 10.210288928 Simplifying x + 10.5 = 10.210288928 Reorder the terms: 10.5 + x = 10.210288928 Solving 10.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 10.210288928 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 10.210288928 + -10.5 x = 10.210288928 + -10.5 Combine like terms: 10.210288928 + -10.5 = -0.289711072 x = -0.289711072 Simplifying x = -0.289711072Subproblem 2
x + 10.5 = -10.210288928 Simplifying x + 10.5 = -10.210288928 Reorder the terms: 10.5 + x = -10.210288928 Solving 10.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -10.210288928 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -10.210288928 + -10.5 x = -10.210288928 + -10.5 Combine like terms: -10.210288928 + -10.5 = -20.710288928 x = -20.710288928 Simplifying x = -20.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.289711072, -20.710288928}
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