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Simplifying 2.3 + 0.17x + -0.0001x2 = 0 Solving 2.3 + 0.17x + -0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0001 the coefficient of the squared term: Divide each side by '-0.0001'. -23000 + -1700x + x2 = 0 Move the constant term to the right: Add '23000' to each side of the equation. -23000 + -1700x + 23000 + x2 = 0 + 23000 Reorder the terms: -23000 + 23000 + -1700x + x2 = 0 + 23000 Combine like terms: -23000 + 23000 = 0 0 + -1700x + x2 = 0 + 23000 -1700x + x2 = 0 + 23000 Combine like terms: 0 + 23000 = 23000 -1700x + x2 = 23000 The x term is -1700x. Take half its coefficient (-850). Square it (722500) and add it to both sides. Add '722500' to each side of the equation. -1700x + 722500 + x2 = 23000 + 722500 Reorder the terms: 722500 + -1700x + x2 = 23000 + 722500 Combine like terms: 23000 + 722500 = 745500 722500 + -1700x + x2 = 745500 Factor a perfect square on the left side: (x + -850)(x + -850) = 745500 Calculate the square root of the right side: 863.423418723 Break this problem into two subproblems by setting (x + -850) equal to 863.423418723 and -863.423418723.Subproblem 1
x + -850 = 863.423418723 Simplifying x + -850 = 863.423418723 Reorder the terms: -850 + x = 863.423418723 Solving -850 + x = 863.423418723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '850' to each side of the equation. -850 + 850 + x = 863.423418723 + 850 Combine like terms: -850 + 850 = 0 0 + x = 863.423418723 + 850 x = 863.423418723 + 850 Combine like terms: 863.423418723 + 850 = 1713.423418723 x = 1713.423418723 Simplifying x = 1713.423418723Subproblem 2
x + -850 = -863.423418723 Simplifying x + -850 = -863.423418723 Reorder the terms: -850 + x = -863.423418723 Solving -850 + x = -863.423418723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '850' to each side of the equation. -850 + 850 + x = -863.423418723 + 850 Combine like terms: -850 + 850 = 0 0 + x = -863.423418723 + 850 x = -863.423418723 + 850 Combine like terms: -863.423418723 + 850 = -13.423418723 x = -13.423418723 Simplifying x = -13.423418723Solution
The solution to the problem is based on the solutions from the subproblems. x = {1713.423418723, -13.423418723}
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