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Simplifying 9x2 = 26x + 80 Reorder the terms: 9x2 = 80 + 26x Solving 9x2 = 80 + 26x Solving for variable 'x'. Reorder the terms: -80 + -26x + 9x2 = 80 + 26x + -80 + -26x Reorder the terms: -80 + -26x + 9x2 = 80 + -80 + 26x + -26x Combine like terms: 80 + -80 = 0 -80 + -26x + 9x2 = 0 + 26x + -26x -80 + -26x + 9x2 = 26x + -26x Combine like terms: 26x + -26x = 0 -80 + -26x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.888888889 + -2.888888889x + x2 = 0 Move the constant term to the right: Add '8.888888889' to each side of the equation. -8.888888889 + -2.888888889x + 8.888888889 + x2 = 0 + 8.888888889 Reorder the terms: -8.888888889 + 8.888888889 + -2.888888889x + x2 = 0 + 8.888888889 Combine like terms: -8.888888889 + 8.888888889 = 0.000000000 0.000000000 + -2.888888889x + x2 = 0 + 8.888888889 -2.888888889x + x2 = 0 + 8.888888889 Combine like terms: 0 + 8.888888889 = 8.888888889 -2.888888889x + x2 = 8.888888889 The x term is -2.888888889x. Take half its coefficient (-1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. -2.888888889x + 2.086419755 + x2 = 8.888888889 + 2.086419755 Reorder the terms: 2.086419755 + -2.888888889x + x2 = 8.888888889 + 2.086419755 Combine like terms: 8.888888889 + 2.086419755 = 10.975308644 2.086419755 + -2.888888889x + x2 = 10.975308644 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 10.975308644 Calculate the square root of the right side: 3.312900337 Break this problem into two subproblems by setting (x + -1.444444445) equal to 3.312900337 and -3.312900337.Subproblem 1
x + -1.444444445 = 3.312900337 Simplifying x + -1.444444445 = 3.312900337 Reorder the terms: -1.444444445 + x = 3.312900337 Solving -1.444444445 + x = 3.312900337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = 3.312900337 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 3.312900337 + 1.444444445 x = 3.312900337 + 1.444444445 Combine like terms: 3.312900337 + 1.444444445 = 4.757344782 x = 4.757344782 Simplifying x = 4.757344782Subproblem 2
x + -1.444444445 = -3.312900337 Simplifying x + -1.444444445 = -3.312900337 Reorder the terms: -1.444444445 + x = -3.312900337 Solving -1.444444445 + x = -3.312900337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = -3.312900337 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -3.312900337 + 1.444444445 x = -3.312900337 + 1.444444445 Combine like terms: -3.312900337 + 1.444444445 = -1.868455892 x = -1.868455892 Simplifying x = -1.868455892Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.757344782, -1.868455892}
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