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Simplifying 0.2x2 + 1.8x + 3.6 = 0 Reorder the terms: 3.6 + 1.8x + 0.2x2 = 0 Solving 3.6 + 1.8x + 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'. 18 + 9x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + 9x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 9x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 9x + x2 = 0 + -18 9x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 9x + x2 = -18 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -18 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -18 + 20.25 Combine like terms: -18 + 20.25 = 2.25 20.25 + 9x + x2 = 2.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 4.5) equal to 1.5 and -1.5.Subproblem 1
x + 4.5 = 1.5 Simplifying x + 4.5 = 1.5 Reorder the terms: 4.5 + x = 1.5 Solving 4.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 1.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 1.5 + -4.5 x = 1.5 + -4.5 Combine like terms: 1.5 + -4.5 = -3 x = -3 Simplifying x = -3Subproblem 2
x + 4.5 = -1.5 Simplifying x + 4.5 = -1.5 Reorder the terms: 4.5 + x = -1.5 Solving 4.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -1.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -1.5 + -4.5 x = -1.5 + -4.5 Combine like terms: -1.5 + -4.5 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3, -6}
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