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Simplifying x2 + 33x + 35 = 0 Reorder the terms: 35 + 33x + x2 = 0 Solving 35 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 33x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 33x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 33x + x2 = 0 + -35 33x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 33x + x2 = -35 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = -35 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -35 + 272.25 Combine like terms: -35 + 272.25 = 237.25 272.25 + 33x + x2 = 237.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 237.25 Calculate the square root of the right side: 15.402921801 Break this problem into two subproblems by setting (x + 16.5) equal to 15.402921801 and -15.402921801.Subproblem 1
x + 16.5 = 15.402921801 Simplifying x + 16.5 = 15.402921801 Reorder the terms: 16.5 + x = 15.402921801 Solving 16.5 + x = 15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 15.402921801 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.402921801 + -16.5 x = 15.402921801 + -16.5 Combine like terms: 15.402921801 + -16.5 = -1.097078199 x = -1.097078199 Simplifying x = -1.097078199Subproblem 2
x + 16.5 = -15.402921801 Simplifying x + 16.5 = -15.402921801 Reorder the terms: 16.5 + x = -15.402921801 Solving 16.5 + x = -15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -15.402921801 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.402921801 + -16.5 x = -15.402921801 + -16.5 Combine like terms: -15.402921801 + -16.5 = -31.902921801 x = -31.902921801 Simplifying x = -31.902921801Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.097078199, -31.902921801}
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