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Simplifying x2 + 17x + -9 = 0 Reorder the terms: -9 + 17x + x2 = 0 Solving -9 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 17x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 17x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 17x + x2 = 0 + 9 17x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 17x + x2 = 9 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 = 9 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 9 + 72.25 Combine like terms: 9 + 72.25 = 81.25 72.25 + 17x + x2 = 81.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 8.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 8.5 = 9.013878189 Simplifying x + 8.5 = 9.013878189 Reorder the terms: 8.5 + x = 9.013878189 Solving 8.5 + x = 9.013878189 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 = 9.013878189 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.013878189 + -8.5 x = 9.013878189 + -8.5 Combine like terms: 9.013878189 + -8.5 = 0.513878189 x = 0.513878189 Simplifying x = 0.513878189Subproblem 2
x + 8.5 = -9.013878189 Simplifying x + 8.5 = -9.013878189 Reorder the terms: 8.5 + x = -9.013878189 Solving 8.5 + x = -9.013878189 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 = -9.013878189 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.013878189 + -8.5 x = -9.013878189 + -8.5 Combine like terms: -9.013878189 + -8.5 = -17.513878189 x = -17.513878189 Simplifying x = -17.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.513878189, -17.513878189}
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