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Simplifying -0.06x2 + 24x + -12 = 0 Reorder the terms: -12 + 24x + -0.06x2 = 0 Solving -12 + 24x + -0.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. 200 + -400x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -400x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -400x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -400x + x2 = 0 + -200 -400x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -400x + x2 = -200 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -200 + 40000 Reorder the terms: 40000 + -400x + x2 = -200 + 40000 Combine like terms: -200 + 40000 = 39800 40000 + -400x + x2 = 39800 Factor a perfect square on the left side: (x + -200)(x + -200) = 39800 Calculate the square root of the right side: 199.499373433 Break this problem into two subproblems by setting (x + -200) equal to 199.499373433 and -199.499373433.Subproblem 1
x + -200 = 199.499373433 Simplifying x + -200 = 199.499373433 Reorder the terms: -200 + x = 199.499373433 Solving -200 + x = 199.499373433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 199.499373433 + 200 Combine like terms: -200 + 200 = 0 0 + x = 199.499373433 + 200 x = 199.499373433 + 200 Combine like terms: 199.499373433 + 200 = 399.499373433 x = 399.499373433 Simplifying x = 399.499373433Subproblem 2
x + -200 = -199.499373433 Simplifying x + -200 = -199.499373433 Reorder the terms: -200 + x = -199.499373433 Solving -200 + x = -199.499373433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -199.499373433 + 200 Combine like terms: -200 + 200 = 0 0 + x = -199.499373433 + 200 x = -199.499373433 + 200 Combine like terms: -199.499373433 + 200 = 0.500626567 x = 0.500626567 Simplifying x = 0.500626567Solution
The solution to the problem is based on the solutions from the subproblems. x = {399.499373433, 0.500626567}
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