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Simplifying x2 + 17x + -216 = 0 Reorder the terms: -216 + 17x + x2 = 0 Solving -216 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 17x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 17x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 17x + x2 = 0 + 216 17x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 17x + x2 = 216 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 = 216 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 216 + 72.25 Combine like terms: 216 + 72.25 = 288.25 72.25 + 17x + x2 = 288.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (x + 8.5) equal to 16.977926846 and -16.977926846.Subproblem 1
x + 8.5 = 16.977926846 Simplifying x + 8.5 = 16.977926846 Reorder the terms: 8.5 + x = 16.977926846 Solving 8.5 + x = 16.977926846 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 = 16.977926846 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 16.977926846 + -8.5 x = 16.977926846 + -8.5 Combine like terms: 16.977926846 + -8.5 = 8.477926846 x = 8.477926846 Simplifying x = 8.477926846Subproblem 2
x + 8.5 = -16.977926846 Simplifying x + 8.5 = -16.977926846 Reorder the terms: 8.5 + x = -16.977926846 Solving 8.5 + x = -16.977926846 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 = -16.977926846 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -16.977926846 + -8.5 x = -16.977926846 + -8.5 Combine like terms: -16.977926846 + -8.5 = -25.477926846 x = -25.477926846 Simplifying x = -25.477926846Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.477926846, -25.477926846}
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