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Simplifying x2 + -17x + -72 = 0 Reorder the terms: -72 + -17x + x2 = 0 Solving -72 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -17x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -17x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -17x + x2 = 0 + 72 -17x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -17x + x2 = 72 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 = 72 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 72 + 72.25 Combine like terms: 72 + 72.25 = 144.25 72.25 + -17x + x2 = 144.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + -8.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + -8.5 = 12.010412149 Simplifying x + -8.5 = 12.010412149 Reorder the terms: -8.5 + x = 12.010412149 Solving -8.5 + x = 12.010412149 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 = 12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 12.010412149 + 8.5 x = 12.010412149 + 8.5 Combine like terms: 12.010412149 + 8.5 = 20.510412149 x = 20.510412149 Simplifying x = 20.510412149Subproblem 2
x + -8.5 = -12.010412149 Simplifying x + -8.5 = -12.010412149 Reorder the terms: -8.5 + x = -12.010412149 Solving -8.5 + x = -12.010412149 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 = -12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -12.010412149 + 8.5 x = -12.010412149 + 8.5 Combine like terms: -12.010412149 + 8.5 = -3.510412149 x = -3.510412149 Simplifying x = -3.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.510412149, -3.510412149}
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