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Simplifying x2 + -17x + -7 = 0 Reorder the terms: -7 + -17x + x2 = 0 Solving -7 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -17x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -17x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -17x + x2 = 0 + 7 -17x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -17x + x2 = 7 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 = 7 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 7 + 72.25 Combine like terms: 7 + 72.25 = 79.25 72.25 + -17x + x2 = 79.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + -8.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + -8.5 = 8.902246907 Simplifying x + -8.5 = 8.902246907 Reorder the terms: -8.5 + x = 8.902246907 Solving -8.5 + x = 8.902246907 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 = 8.902246907 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.902246907 + 8.5 x = 8.902246907 + 8.5 Combine like terms: 8.902246907 + 8.5 = 17.402246907 x = 17.402246907 Simplifying x = 17.402246907Subproblem 2
x + -8.5 = -8.902246907 Simplifying x + -8.5 = -8.902246907 Reorder the terms: -8.5 + x = -8.902246907 Solving -8.5 + x = -8.902246907 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 = -8.902246907 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.902246907 + 8.5 x = -8.902246907 + 8.5 Combine like terms: -8.902246907 + 8.5 = -0.402246907 x = -0.402246907 Simplifying x = -0.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.402246907, -0.402246907}
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