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Simplifying 7x2 + -49x + 17 = 0 Reorder the terms: 17 + -49x + 7x2 = 0 Solving 17 + -49x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.428571429 + -7x + x2 = 0 Move the constant term to the right: Add '-2.428571429' to each side of the equation. 2.428571429 + -7x + -2.428571429 + x2 = 0 + -2.428571429 Reorder the terms: 2.428571429 + -2.428571429 + -7x + x2 = 0 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + -7x + x2 = 0 + -2.428571429 -7x + x2 = 0 + -2.428571429 Combine like terms: 0 + -2.428571429 = -2.428571429 -7x + x2 = -2.428571429 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -2.428571429 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -2.428571429 + 12.25 Combine like terms: -2.428571429 + 12.25 = 9.821428571 12.25 + -7x + x2 = 9.821428571 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 9.821428571 Calculate the square root of the right side: 3.133915853 Break this problem into two subproblems by setting (x + -3.5) equal to 3.133915853 and -3.133915853.Subproblem 1
x + -3.5 = 3.133915853 Simplifying x + -3.5 = 3.133915853 Reorder the terms: -3.5 + x = 3.133915853 Solving -3.5 + x = 3.133915853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.133915853 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.133915853 + 3.5 x = 3.133915853 + 3.5 Combine like terms: 3.133915853 + 3.5 = 6.633915853 x = 6.633915853 Simplifying x = 6.633915853Subproblem 2
x + -3.5 = -3.133915853 Simplifying x + -3.5 = -3.133915853 Reorder the terms: -3.5 + x = -3.133915853 Solving -3.5 + x = -3.133915853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.133915853 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.133915853 + 3.5 x = -3.133915853 + 3.5 Combine like terms: -3.133915853 + 3.5 = 0.366084147 x = 0.366084147 Simplifying x = 0.366084147Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.633915853, 0.366084147}
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