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Simplifying x2 + 3x + -408 = 0 Reorder the terms: -408 + 3x + x2 = 0 Solving -408 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '408' to each side of the equation. -408 + 3x + 408 + x2 = 0 + 408 Reorder the terms: -408 + 408 + 3x + x2 = 0 + 408 Combine like terms: -408 + 408 = 0 0 + 3x + x2 = 0 + 408 3x + x2 = 0 + 408 Combine like terms: 0 + 408 = 408 3x + x2 = 408 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 = 408 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 408 + 2.25 Combine like terms: 408 + 2.25 = 410.25 2.25 + 3x + x2 = 410.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 410.25 Calculate the square root of the right side: 20.254629101 Break this problem into two subproblems by setting (x + 1.5) equal to 20.254629101 and -20.254629101.Subproblem 1
x + 1.5 = 20.254629101 Simplifying x + 1.5 = 20.254629101 Reorder the terms: 1.5 + x = 20.254629101 Solving 1.5 + x = 20.254629101 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 = 20.254629101 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 20.254629101 + -1.5 x = 20.254629101 + -1.5 Combine like terms: 20.254629101 + -1.5 = 18.754629101 x = 18.754629101 Simplifying x = 18.754629101Subproblem 2
x + 1.5 = -20.254629101 Simplifying x + 1.5 = -20.254629101 Reorder the terms: 1.5 + x = -20.254629101 Solving 1.5 + x = -20.254629101 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 = -20.254629101 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -20.254629101 + -1.5 x = -20.254629101 + -1.5 Combine like terms: -20.254629101 + -1.5 = -21.754629101 x = -21.754629101 Simplifying x = -21.754629101Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.754629101, -21.754629101}
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