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Simplifying -0.012x2 + -0.24x + 8006.3 = 0 Reorder the terms: 8006.3 + -0.24x + -0.012x2 = 0 Solving 8006.3 + -0.24x + -0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -667191.6667 + 20x + x2 = 0 Move the constant term to the right: Add '667191.6667' to each side of the equation. -667191.6667 + 20x + 667191.6667 + x2 = 0 + 667191.6667 Reorder the terms: -667191.6667 + 667191.6667 + 20x + x2 = 0 + 667191.6667 Combine like terms: -667191.6667 + 667191.6667 = 0.0000 0.0000 + 20x + x2 = 0 + 667191.6667 20x + x2 = 0 + 667191.6667 Combine like terms: 0 + 667191.6667 = 667191.6667 20x + x2 = 667191.6667 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 667191.6667 + 100 Reorder the terms: 100 + 20x + x2 = 667191.6667 + 100 Combine like terms: 667191.6667 + 100 = 667291.6667 100 + 20x + x2 = 667291.6667 Factor a perfect square on the left side: (x + 10)(x + 10) = 667291.6667 Calculate the square root of the right side: 816.879224059 Break this problem into two subproblems by setting (x + 10) equal to 816.879224059 and -816.879224059.Subproblem 1
x + 10 = 816.879224059 Simplifying x + 10 = 816.879224059 Reorder the terms: 10 + x = 816.879224059 Solving 10 + x = 816.879224059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 816.879224059 + -10 Combine like terms: 10 + -10 = 0 0 + x = 816.879224059 + -10 x = 816.879224059 + -10 Combine like terms: 816.879224059 + -10 = 806.879224059 x = 806.879224059 Simplifying x = 806.879224059Subproblem 2
x + 10 = -816.879224059 Simplifying x + 10 = -816.879224059 Reorder the terms: 10 + x = -816.879224059 Solving 10 + x = -816.879224059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -816.879224059 + -10 Combine like terms: 10 + -10 = 0 0 + x = -816.879224059 + -10 x = -816.879224059 + -10 Combine like terms: -816.879224059 + -10 = -826.879224059 x = -826.879224059 Simplifying x = -826.879224059Solution
The solution to the problem is based on the solutions from the subproblems. x = {806.879224059, -826.879224059}
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