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Simplifying 4x + (x + 6)(x + 3) = 0 Reorder the terms: 4x + (6 + x)(x + 3) = 0 Reorder the terms: 4x + (6 + x)(3 + x) = 0 Multiply (6 + x) * (3 + x) 4x + (6(3 + x) + x(3 + x)) = 0 4x + ((3 * 6 + x * 6) + x(3 + x)) = 0 4x + ((18 + 6x) + x(3 + x)) = 0 4x + (18 + 6x + (3 * x + x * x)) = 0 4x + (18 + 6x + (3x + x2)) = 0 Combine like terms: 6x + 3x = 9x 4x + (18 + 9x + x2) = 0 Reorder the terms: 18 + 4x + 9x + x2 = 0 Combine like terms: 4x + 9x = 13x 18 + 13x + x2 = 0 Solving 18 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 13x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 13x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 13x + x2 = 0 + -18 13x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 13x + x2 = -18 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -18 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -18 + 42.25 Combine like terms: -18 + 42.25 = 24.25 42.25 + 13x + x2 = 24.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 6.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 6.5 = 4.924428901 Simplifying x + 6.5 = 4.924428901 Reorder the terms: 6.5 + x = 4.924428901 Solving 6.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 4.924428901 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 4.924428901 + -6.5 x = 4.924428901 + -6.5 Combine like terms: 4.924428901 + -6.5 = -1.575571099 x = -1.575571099 Simplifying x = -1.575571099Subproblem 2
x + 6.5 = -4.924428901 Simplifying x + 6.5 = -4.924428901 Reorder the terms: 6.5 + x = -4.924428901 Solving 6.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -4.924428901 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -4.924428901 + -6.5 x = -4.924428901 + -6.5 Combine like terms: -4.924428901 + -6.5 = -11.424428901 x = -11.424428901 Simplifying x = -11.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.575571099, -11.424428901}
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