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Simplifying 17x2 + 92x + -206 = 0 Reorder the terms: -206 + 92x + 17x2 = 0 Solving -206 + 92x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -12.11764706 + 5.411764706x + x2 = 0 Move the constant term to the right: Add '12.11764706' to each side of the equation. -12.11764706 + 5.411764706x + 12.11764706 + x2 = 0 + 12.11764706 Reorder the terms: -12.11764706 + 12.11764706 + 5.411764706x + x2 = 0 + 12.11764706 Combine like terms: -12.11764706 + 12.11764706 = 0.00000000 0.00000000 + 5.411764706x + x2 = 0 + 12.11764706 5.411764706x + x2 = 0 + 12.11764706 Combine like terms: 0 + 12.11764706 = 12.11764706 5.411764706x + x2 = 12.11764706 The x term is 5.411764706x. Take half its coefficient (2.705882353). Square it (7.321799308) and add it to both sides. Add '7.321799308' to each side of the equation. 5.411764706x + 7.321799308 + x2 = 12.11764706 + 7.321799308 Reorder the terms: 7.321799308 + 5.411764706x + x2 = 12.11764706 + 7.321799308 Combine like terms: 12.11764706 + 7.321799308 = 19.439446368 7.321799308 + 5.411764706x + x2 = 19.439446368 Factor a perfect square on the left side: (x + 2.705882353)(x + 2.705882353) = 19.439446368 Calculate the square root of the right side: 4.409018753 Break this problem into two subproblems by setting (x + 2.705882353) equal to 4.409018753 and -4.409018753.Subproblem 1
x + 2.705882353 = 4.409018753 Simplifying x + 2.705882353 = 4.409018753 Reorder the terms: 2.705882353 + x = 4.409018753 Solving 2.705882353 + x = 4.409018753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.705882353' to each side of the equation. 2.705882353 + -2.705882353 + x = 4.409018753 + -2.705882353 Combine like terms: 2.705882353 + -2.705882353 = 0.000000000 0.000000000 + x = 4.409018753 + -2.705882353 x = 4.409018753 + -2.705882353 Combine like terms: 4.409018753 + -2.705882353 = 1.7031364 x = 1.7031364 Simplifying x = 1.7031364Subproblem 2
x + 2.705882353 = -4.409018753 Simplifying x + 2.705882353 = -4.409018753 Reorder the terms: 2.705882353 + x = -4.409018753 Solving 2.705882353 + x = -4.409018753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.705882353' to each side of the equation. 2.705882353 + -2.705882353 + x = -4.409018753 + -2.705882353 Combine like terms: 2.705882353 + -2.705882353 = 0.000000000 0.000000000 + x = -4.409018753 + -2.705882353 x = -4.409018753 + -2.705882353 Combine like terms: -4.409018753 + -2.705882353 = -7.114901106 x = -7.114901106 Simplifying x = -7.114901106Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7031364, -7.114901106}
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