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Simplifying 9x2 + -12167x + -512 = 0 Reorder the terms: -512 + -12167x + 9x2 = 0 Solving -512 + -12167x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -56.88888889 + -1351.888889x + x2 = 0 Move the constant term to the right: Add '56.88888889' to each side of the equation. -56.88888889 + -1351.888889x + 56.88888889 + x2 = 0 + 56.88888889 Reorder the terms: -56.88888889 + 56.88888889 + -1351.888889x + x2 = 0 + 56.88888889 Combine like terms: -56.88888889 + 56.88888889 = 0.00000000 0.00000000 + -1351.888889x + x2 = 0 + 56.88888889 -1351.888889x + x2 = 0 + 56.88888889 Combine like terms: 0 + 56.88888889 = 56.88888889 -1351.888889x + x2 = 56.88888889 The x term is -1351.888889x. Take half its coefficient (-675.9444445). Square it (456900.8921) and add it to both sides. Add '456900.8921' to each side of the equation. -1351.888889x + 456900.8921 + x2 = 56.88888889 + 456900.8921 Reorder the terms: 456900.8921 + -1351.888889x + x2 = 56.88888889 + 456900.8921 Combine like terms: 56.88888889 + 456900.8921 = 456957.78098889 456900.8921 + -1351.888889x + x2 = 456957.78098889 Factor a perfect square on the left side: (x + -675.9444445)(x + -675.9444445) = 456957.78098889 Calculate the square root of the right side: 675.986524266 Break this problem into two subproblems by setting (x + -675.9444445) equal to 675.986524266 and -675.986524266.Subproblem 1
x + -675.9444445 = 675.986524266 Simplifying x + -675.9444445 = 675.986524266 Reorder the terms: -675.9444445 + x = 675.986524266 Solving -675.9444445 + x = 675.986524266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '675.9444445' to each side of the equation. -675.9444445 + 675.9444445 + x = 675.986524266 + 675.9444445 Combine like terms: -675.9444445 + 675.9444445 = 0.0000000 0.0000000 + x = 675.986524266 + 675.9444445 x = 675.986524266 + 675.9444445 Combine like terms: 675.986524266 + 675.9444445 = 1351.930968766 x = 1351.930968766 Simplifying x = 1351.930968766Subproblem 2
x + -675.9444445 = -675.986524266 Simplifying x + -675.9444445 = -675.986524266 Reorder the terms: -675.9444445 + x = -675.986524266 Solving -675.9444445 + x = -675.986524266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '675.9444445' to each side of the equation. -675.9444445 + 675.9444445 + x = -675.986524266 + 675.9444445 Combine like terms: -675.9444445 + 675.9444445 = 0.0000000 0.0000000 + x = -675.986524266 + 675.9444445 x = -675.986524266 + 675.9444445 Combine like terms: -675.986524266 + 675.9444445 = -0.042079766 x = -0.042079766 Simplifying x = -0.042079766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1351.930968766, -0.042079766}
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