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Simplifying 0.2x2 + -12x = -50 Reorder the terms: -12x + 0.2x2 = -50 Solving -12x + 0.2x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + -12x + 0.2x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -12x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 250 + -60x + x2 = 0 Move the constant term to the right: Add '-250' to each side of the equation. 250 + -60x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -60x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -60x + x2 = 0 + -250 -60x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -60x + x2 = -250 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -250 + 900 Reorder the terms: 900 + -60x + x2 = -250 + 900 Combine like terms: -250 + 900 = 650 900 + -60x + x2 = 650 Factor a perfect square on the left side: (x + -30)(x + -30) = 650 Calculate the square root of the right side: 25.495097568 Break this problem into two subproblems by setting (x + -30) equal to 25.495097568 and -25.495097568.Subproblem 1
x + -30 = 25.495097568 Simplifying x + -30 = 25.495097568 Reorder the terms: -30 + x = 25.495097568 Solving -30 + x = 25.495097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 25.495097568 + 30 Combine like terms: -30 + 30 = 0 0 + x = 25.495097568 + 30 x = 25.495097568 + 30 Combine like terms: 25.495097568 + 30 = 55.495097568 x = 55.495097568 Simplifying x = 55.495097568Subproblem 2
x + -30 = -25.495097568 Simplifying x + -30 = -25.495097568 Reorder the terms: -30 + x = -25.495097568 Solving -30 + x = -25.495097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -25.495097568 + 30 Combine like terms: -30 + 30 = 0 0 + x = -25.495097568 + 30 x = -25.495097568 + 30 Combine like terms: -25.495097568 + 30 = 4.504902432 x = 4.504902432 Simplifying x = 4.504902432Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.495097568, 4.504902432}
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