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Simplifying 9x2 + -94x + 225 = 0 Reorder the terms: 225 + -94x + 9x2 = 0 Solving 225 + -94x + 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'. 25 + -10.44444444x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -10.44444444x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -10.44444444x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -10.44444444x + x2 = 0 + -25 -10.44444444x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -10.44444444x + x2 = -25 The x term is -10.44444444x. Take half its coefficient (-5.22222222). Square it (27.27160492) and add it to both sides. Add '27.27160492' to each side of the equation. -10.44444444x + 27.27160492 + x2 = -25 + 27.27160492 Reorder the terms: 27.27160492 + -10.44444444x + x2 = -25 + 27.27160492 Combine like terms: -25 + 27.27160492 = 2.27160492 27.27160492 + -10.44444444x + x2 = 2.27160492 Factor a perfect square on the left side: (x + -5.22222222)(x + -5.22222222) = 2.27160492 Calculate the square root of the right side: 1.507184435 Break this problem into two subproblems by setting (x + -5.22222222) equal to 1.507184435 and -1.507184435.Subproblem 1
x + -5.22222222 = 1.507184435 Simplifying x + -5.22222222 = 1.507184435 Reorder the terms: -5.22222222 + x = 1.507184435 Solving -5.22222222 + x = 1.507184435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.22222222' to each side of the equation. -5.22222222 + 5.22222222 + x = 1.507184435 + 5.22222222 Combine like terms: -5.22222222 + 5.22222222 = 0.00000000 0.00000000 + x = 1.507184435 + 5.22222222 x = 1.507184435 + 5.22222222 Combine like terms: 1.507184435 + 5.22222222 = 6.729406655 x = 6.729406655 Simplifying x = 6.729406655Subproblem 2
x + -5.22222222 = -1.507184435 Simplifying x + -5.22222222 = -1.507184435 Reorder the terms: -5.22222222 + x = -1.507184435 Solving -5.22222222 + x = -1.507184435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.22222222' to each side of the equation. -5.22222222 + 5.22222222 + x = -1.507184435 + 5.22222222 Combine like terms: -5.22222222 + 5.22222222 = 0.00000000 0.00000000 + x = -1.507184435 + 5.22222222 x = -1.507184435 + 5.22222222 Combine like terms: -1.507184435 + 5.22222222 = 3.715037785 x = 3.715037785 Simplifying x = 3.715037785Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.729406655, 3.715037785}
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