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Simplifying 17x2 + -2000x + 4000 = 0 Reorder the terms: 4000 + -2000x + 17x2 = 0 Solving 4000 + -2000x + 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'. 235.2941176 + -117.6470588x + x2 = 0 Move the constant term to the right: Add '-235.2941176' to each side of the equation. 235.2941176 + -117.6470588x + -235.2941176 + x2 = 0 + -235.2941176 Reorder the terms: 235.2941176 + -235.2941176 + -117.6470588x + x2 = 0 + -235.2941176 Combine like terms: 235.2941176 + -235.2941176 = 0.0000000 0.0000000 + -117.6470588x + x2 = 0 + -235.2941176 -117.6470588x + x2 = 0 + -235.2941176 Combine like terms: 0 + -235.2941176 = -235.2941176 -117.6470588x + x2 = -235.2941176 The x term is -117.6470588x. Take half its coefficient (-58.8235294). Square it (3460.207611) and add it to both sides. Add '3460.207611' to each side of the equation. -117.6470588x + 3460.207611 + x2 = -235.2941176 + 3460.207611 Reorder the terms: 3460.207611 + -117.6470588x + x2 = -235.2941176 + 3460.207611 Combine like terms: -235.2941176 + 3460.207611 = 3224.9134934 3460.207611 + -117.6470588x + x2 = 3224.9134934 Factor a perfect square on the left side: (x + -58.8235294)(x + -58.8235294) = 3224.9134934 Calculate the square root of the right side: 56.788321805 Break this problem into two subproblems by setting (x + -58.8235294) equal to 56.788321805 and -56.788321805.Subproblem 1
x + -58.8235294 = 56.788321805 Simplifying x + -58.8235294 = 56.788321805 Reorder the terms: -58.8235294 + x = 56.788321805 Solving -58.8235294 + x = 56.788321805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.8235294' to each side of the equation. -58.8235294 + 58.8235294 + x = 56.788321805 + 58.8235294 Combine like terms: -58.8235294 + 58.8235294 = 0.0000000 0.0000000 + x = 56.788321805 + 58.8235294 x = 56.788321805 + 58.8235294 Combine like terms: 56.788321805 + 58.8235294 = 115.611851205 x = 115.611851205 Simplifying x = 115.611851205Subproblem 2
x + -58.8235294 = -56.788321805 Simplifying x + -58.8235294 = -56.788321805 Reorder the terms: -58.8235294 + x = -56.788321805 Solving -58.8235294 + x = -56.788321805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.8235294' to each side of the equation. -58.8235294 + 58.8235294 + x = -56.788321805 + 58.8235294 Combine like terms: -58.8235294 + 58.8235294 = 0.0000000 0.0000000 + x = -56.788321805 + 58.8235294 x = -56.788321805 + 58.8235294 Combine like terms: -56.788321805 + 58.8235294 = 2.035207595 x = 2.035207595 Simplifying x = 2.035207595Solution
The solution to the problem is based on the solutions from the subproblems. x = {115.611851205, 2.035207595}
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