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Simplifying x2 + 17x + 13 = 0 Reorder the terms: 13 + 17x + x2 = 0 Solving 13 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 17x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 17x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 17x + x2 = 0 + -13 17x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 17x + x2 = -13 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 = -13 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -13 + 72.25 Combine like terms: -13 + 72.25 = 59.25 72.25 + 17x + x2 = 59.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 8.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 8.5 = 7.697402159 Simplifying x + 8.5 = 7.697402159 Reorder the terms: 8.5 + x = 7.697402159 Solving 8.5 + x = 7.697402159 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 = 7.697402159 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.697402159 + -8.5 x = 7.697402159 + -8.5 Combine like terms: 7.697402159 + -8.5 = -0.802597841 x = -0.802597841 Simplifying x = -0.802597841Subproblem 2
x + 8.5 = -7.697402159 Simplifying x + 8.5 = -7.697402159 Reorder the terms: 8.5 + x = -7.697402159 Solving 8.5 + x = -7.697402159 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 = -7.697402159 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.697402159 + -8.5 x = -7.697402159 + -8.5 Combine like terms: -7.697402159 + -8.5 = -16.197402159 x = -16.197402159 Simplifying x = -16.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.802597841, -16.197402159}
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