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Simplifying (x2) + 3x = 308 x2 + 3x = 308 Reorder the terms: 3x + x2 = 308 Solving 3x + x2 = 308 Solving for variable 'x'. Reorder the terms: -308 + 3x + x2 = 308 + -308 Combine like terms: 308 + -308 = 0 -308 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + 3x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + 3x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 3x + x2 = 0 + 308 3x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 3x + x2 = 308 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 308 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 308 + 2.25 Combine like terms: 308 + 2.25 = 310.25 2.25 + 3x + x2 = 310.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 310.25 Calculate the square root of the right side: 17.613914954 Break this problem into two subproblems by setting (x + 1.5) equal to 17.613914954 and -17.613914954.Subproblem 1
x + 1.5 = 17.613914954 Simplifying x + 1.5 = 17.613914954 Reorder the terms: 1.5 + x = 17.613914954 Solving 1.5 + x = 17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 17.613914954 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.613914954 + -1.5 x = 17.613914954 + -1.5 Combine like terms: 17.613914954 + -1.5 = 16.113914954 x = 16.113914954 Simplifying x = 16.113914954Subproblem 2
x + 1.5 = -17.613914954 Simplifying x + 1.5 = -17.613914954 Reorder the terms: 1.5 + x = -17.613914954 Solving 1.5 + x = -17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -17.613914954 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.613914954 + -1.5 x = -17.613914954 + -1.5 Combine like terms: -17.613914954 + -1.5 = -19.113914954 x = -19.113914954 Simplifying x = -19.113914954Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.113914954, -19.113914954}
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