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Simplifying x2 + 3x + -336 = 0 Reorder the terms: -336 + 3x + x2 = 0 Solving -336 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + 3x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + 3x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 3x + x2 = 0 + 336 3x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 3x + x2 = 336 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 = 336 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 336 + 2.25 Combine like terms: 336 + 2.25 = 338.25 2.25 + 3x + x2 = 338.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 338.25 Calculate the square root of the right side: 18.391574158 Break this problem into two subproblems by setting (x + 1.5) equal to 18.391574158 and -18.391574158.Subproblem 1
x + 1.5 = 18.391574158 Simplifying x + 1.5 = 18.391574158 Reorder the terms: 1.5 + x = 18.391574158 Solving 1.5 + x = 18.391574158 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 = 18.391574158 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 18.391574158 + -1.5 x = 18.391574158 + -1.5 Combine like terms: 18.391574158 + -1.5 = 16.891574158 x = 16.891574158 Simplifying x = 16.891574158Subproblem 2
x + 1.5 = -18.391574158 Simplifying x + 1.5 = -18.391574158 Reorder the terms: 1.5 + x = -18.391574158 Solving 1.5 + x = -18.391574158 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 = -18.391574158 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -18.391574158 + -1.5 x = -18.391574158 + -1.5 Combine like terms: -18.391574158 + -1.5 = -19.891574158 x = -19.891574158 Simplifying x = -19.891574158Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.891574158, -19.891574158}
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