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Simplifying x2 = 17x + -3 Reorder the terms: x2 = -3 + 17x Solving x2 = -3 + 17x Solving for variable 'x'. Reorder the terms: 3 + -17x + x2 = -3 + 17x + 3 + -17x Reorder the terms: 3 + -17x + x2 = -3 + 3 + 17x + -17x Combine like terms: -3 + 3 = 0 3 + -17x + x2 = 0 + 17x + -17x 3 + -17x + x2 = 17x + -17x Combine like terms: 17x + -17x = 0 3 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -17x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -17x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -17x + x2 = 0 + -3 -17x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -17x + x2 = -3 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 = -3 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -3 + 72.25 Combine like terms: -3 + 72.25 = 69.25 72.25 + -17x + x2 = 69.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -8.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -8.5 = 8.321658489 Simplifying x + -8.5 = 8.321658489 Reorder the terms: -8.5 + x = 8.321658489 Solving -8.5 + x = 8.321658489 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 = 8.321658489 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.321658489 + 8.5 x = 8.321658489 + 8.5 Combine like terms: 8.321658489 + 8.5 = 16.821658489 x = 16.821658489 Simplifying x = 16.821658489Subproblem 2
x + -8.5 = -8.321658489 Simplifying x + -8.5 = -8.321658489 Reorder the terms: -8.5 + x = -8.321658489 Solving -8.5 + x = -8.321658489 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 = -8.321658489 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.321658489 + 8.5 x = -8.321658489 + 8.5 Combine like terms: -8.321658489 + 8.5 = 0.178341511 x = 0.178341511 Simplifying x = 0.178341511Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.821658489, 0.178341511}
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