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Simplifying x2 + 3x + -364 = 0 Reorder the terms: -364 + 3x + x2 = 0 Solving -364 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '364' to each side of the equation. -364 + 3x + 364 + x2 = 0 + 364 Reorder the terms: -364 + 364 + 3x + x2 = 0 + 364 Combine like terms: -364 + 364 = 0 0 + 3x + x2 = 0 + 364 3x + x2 = 0 + 364 Combine like terms: 0 + 364 = 364 3x + x2 = 364 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 = 364 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 364 + 2.25 Combine like terms: 364 + 2.25 = 366.25 2.25 + 3x + x2 = 366.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 366.25 Calculate the square root of the right side: 19.137659209 Break this problem into two subproblems by setting (x + 1.5) equal to 19.137659209 and -19.137659209.Subproblem 1
x + 1.5 = 19.137659209 Simplifying x + 1.5 = 19.137659209 Reorder the terms: 1.5 + x = 19.137659209 Solving 1.5 + x = 19.137659209 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 = 19.137659209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 19.137659209 + -1.5 x = 19.137659209 + -1.5 Combine like terms: 19.137659209 + -1.5 = 17.637659209 x = 17.637659209 Simplifying x = 17.637659209Subproblem 2
x + 1.5 = -19.137659209 Simplifying x + 1.5 = -19.137659209 Reorder the terms: 1.5 + x = -19.137659209 Solving 1.5 + x = -19.137659209 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 = -19.137659209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -19.137659209 + -1.5 x = -19.137659209 + -1.5 Combine like terms: -19.137659209 + -1.5 = -20.637659209 x = -20.637659209 Simplifying x = -20.637659209Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.637659209, -20.637659209}
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