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Simplifying x2 + (4 * 6x + 3x) + -5 = 3 Multiply 4 * 6 x2 + (24x + 3x) + -5 = 3 Combine like terms: 24x + 3x = 27x x2 + (27x) + -5 = 3 x2 + (27x) + -5 = 3 Reorder the terms: -5 + (27x) + x2 = 3 Solving -5 + (27x) + x2 = 3 Solving for variable 'x'. Reorder the terms: -5 + -3 + (27x) + x2 = 3 + -3 Combine like terms: -5 + -3 = -8 -8 + (27x) + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -8 + (27x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + (27x) + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + (27x) + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + (27x) + x2 = 0 + 8 (27x) + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 (27x) + x2 = 8 The x term is (27x). Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. (27x) + 182.25 + x2 = 8 + 182.25 Reorder the terms: 182.25 + (27x) + x2 = 8 + 182.25 Combine like terms: 8 + 182.25 = 190.25 182.25 + (27x) + x2 = 190.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 13.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 13.5 = 13.793114224 Simplifying x + 13.5 = 13.793114224 Reorder the terms: 13.5 + x = 13.793114224 Solving 13.5 + x = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.793114224 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.793114224 + -13.5 x = 13.793114224 + -13.5 Combine like terms: 13.793114224 + -13.5 = 0.293114224 x = 0.293114224 Simplifying x = 0.293114224Subproblem 2
x + 13.5 = -13.793114224 Simplifying x + 13.5 = -13.793114224 Reorder the terms: 13.5 + x = -13.793114224 Solving 13.5 + x = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.793114224 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.793114224 + -13.5 x = -13.793114224 + -13.5 Combine like terms: -13.793114224 + -13.5 = -27.293114224 x = -27.293114224 Simplifying x = -27.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293114224, -27.293114224}
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