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Simplifying x2 + 16 = (17x + -4) Reorder the terms: 16 + x2 = (17x + -4) Reorder the terms: 16 + x2 = (-4 + 17x) Remove parenthesis around (-4 + 17x) 16 + x2 = -4 + 17x Solving 16 + x2 = -4 + 17x Solving for variable 'x'. Reorder the terms: 16 + 4 + -17x + x2 = -4 + 17x + 4 + -17x Combine like terms: 16 + 4 = 20 20 + -17x + x2 = -4 + 17x + 4 + -17x Reorder the terms: 20 + -17x + x2 = -4 + 4 + 17x + -17x Combine like terms: -4 + 4 = 0 20 + -17x + x2 = 0 + 17x + -17x 20 + -17x + x2 = 17x + -17x Combine like terms: 17x + -17x = 0 20 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -17x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -17x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -17x + x2 = 0 + -20 -17x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -17x + x2 = -20 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 = -20 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -20 + 72.25 Combine like terms: -20 + 72.25 = 52.25 72.25 + -17x + x2 = 52.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -8.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -8.5 = 7.228416147 Simplifying x + -8.5 = 7.228416147 Reorder the terms: -8.5 + x = 7.228416147 Solving -8.5 + x = 7.228416147 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 = 7.228416147 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.228416147 + 8.5 x = 7.228416147 + 8.5 Combine like terms: 7.228416147 + 8.5 = 15.728416147 x = 15.728416147 Simplifying x = 15.728416147Subproblem 2
x + -8.5 = -7.228416147 Simplifying x + -8.5 = -7.228416147 Reorder the terms: -8.5 + x = -7.228416147 Solving -8.5 + x = -7.228416147 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 = -7.228416147 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.228416147 + 8.5 x = -7.228416147 + 8.5 Combine like terms: -7.228416147 + 8.5 = 1.271583853 x = 1.271583853 Simplifying x = 1.271583853Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.728416147, 1.271583853}
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