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Simplifying x2 + 17x + 37 = 0 Reorder the terms: 37 + 17x + x2 = 0 Solving 37 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 17x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 17x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 17x + x2 = 0 + -37 17x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 17x + x2 = -37 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -37 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -37 + 72.25 Combine like terms: -37 + 72.25 = 35.25 72.25 + 17x + x2 = 35.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 8.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 8.5 = 5.937171044 Simplifying x + 8.5 = 5.937171044 Reorder the terms: 8.5 + x = 5.937171044 Solving 8.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 5.937171044 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 5.937171044 + -8.5 x = 5.937171044 + -8.5 Combine like terms: 5.937171044 + -8.5 = -2.562828956 x = -2.562828956 Simplifying x = -2.562828956Subproblem 2
x + 8.5 = -5.937171044 Simplifying x + 8.5 = -5.937171044 Reorder the terms: 8.5 + x = -5.937171044 Solving 8.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -5.937171044 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -5.937171044 + -8.5 x = -5.937171044 + -8.5 Combine like terms: -5.937171044 + -8.5 = -14.437171044 x = -14.437171044 Simplifying x = -14.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.562828956, -14.437171044}
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