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Simplifying 0.2x2 + -0.8x + -4.2 = 0 Reorder the terms: -4.2 + -0.8x + 0.2x2 = 0 Solving -4.2 + -0.8x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -21 + -4x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -4x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -4x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4x + x2 = 0 + 21 -4x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -4x + x2 = 21 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 21 + 4 Reorder the terms: 4 + -4x + x2 = 21 + 4 Combine like terms: 21 + 4 = 25 4 + -4x + x2 = 25 Factor a perfect square on the left side: (x + -2)(x + -2) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -2) equal to 5 and -5.Subproblem 1
x + -2 = 5 Simplifying x + -2 = 5 Reorder the terms: -2 + x = 5 Solving -2 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5 + 2 x = 5 + 2 Combine like terms: 5 + 2 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -2 = -5 Simplifying x + -2 = -5 Reorder the terms: -2 + x = -5 Solving -2 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5 + 2 x = -5 + 2 Combine like terms: -5 + 2 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, -3}
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