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Simplifying 0.5x2 + 1.5x + -480 = 0 Reorder the terms: -480 + 1.5x + 0.5x2 = 0 Solving -480 + 1.5x + 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'. -960 + 3x + x2 = 0 Move the constant term to the right: Add '960' to each side of the equation. -960 + 3x + 960 + x2 = 0 + 960 Reorder the terms: -960 + 960 + 3x + x2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + 3x + x2 = 0 + 960 3x + x2 = 0 + 960 Combine like terms: 0 + 960 = 960 3x + x2 = 960 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 960 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 960 + 2.25 Combine like terms: 960 + 2.25 = 962.25 2.25 + 3x + x2 = 962.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 962.25 Calculate the square root of the right side: 31.020154738 Break this problem into two subproblems by setting (x + 1.5) equal to 31.020154738 and -31.020154738.Subproblem 1
x + 1.5 = 31.020154738 Simplifying x + 1.5 = 31.020154738 Reorder the terms: 1.5 + x = 31.020154738 Solving 1.5 + x = 31.020154738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 31.020154738 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 31.020154738 + -1.5 x = 31.020154738 + -1.5 Combine like terms: 31.020154738 + -1.5 = 29.520154738 x = 29.520154738 Simplifying x = 29.520154738Subproblem 2
x + 1.5 = -31.020154738 Simplifying x + 1.5 = -31.020154738 Reorder the terms: 1.5 + x = -31.020154738 Solving 1.5 + x = -31.020154738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -31.020154738 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -31.020154738 + -1.5 x = -31.020154738 + -1.5 Combine like terms: -31.020154738 + -1.5 = -32.520154738 x = -32.520154738 Simplifying x = -32.520154738Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.520154738, -32.520154738}
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