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Simplifying 0.5x2 + -4.5x + 9 = 0 Reorder the terms: 9 + -4.5x + 0.5x2 = 0 Solving 9 + -4.5x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 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 = 6 x = 6 Simplifying x = 6Subproblem 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 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 3}
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