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Simplifying x2 + -17x + -171 = 0 Reorder the terms: -171 + -17x + x2 = 0 Solving -171 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + -17x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + -17x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + -17x + x2 = 0 + 171 -17x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 -17x + x2 = 171 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 = 171 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 171 + 72.25 Combine like terms: 171 + 72.25 = 243.25 72.25 + -17x + x2 = 243.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 243.25 Calculate the square root of the right side: 15.59647396 Break this problem into two subproblems by setting (x + -8.5) equal to 15.59647396 and -15.59647396.Subproblem 1
x + -8.5 = 15.59647396 Simplifying x + -8.5 = 15.59647396 Reorder the terms: -8.5 + x = 15.59647396 Solving -8.5 + x = 15.59647396 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 = 15.59647396 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 15.59647396 + 8.5 x = 15.59647396 + 8.5 Combine like terms: 15.59647396 + 8.5 = 24.09647396 x = 24.09647396 Simplifying x = 24.09647396Subproblem 2
x + -8.5 = -15.59647396 Simplifying x + -8.5 = -15.59647396 Reorder the terms: -8.5 + x = -15.59647396 Solving -8.5 + x = -15.59647396 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 = -15.59647396 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -15.59647396 + 8.5 x = -15.59647396 + 8.5 Combine like terms: -15.59647396 + 8.5 = -7.09647396 x = -7.09647396 Simplifying x = -7.09647396Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.09647396, -7.09647396}
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