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Simplifying 0.5x2 + -1.5x = 1275 Reorder the terms: -1.5x + 0.5x2 = 1275 Solving -1.5x + 0.5x2 = 1275 Solving for variable 'x'. Reorder the terms: -1275 + -1.5x + 0.5x2 = 1275 + -1275 Combine like terms: 1275 + -1275 = 0 -1275 + -1.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -2550 + -3x + x2 = 0 Move the constant term to the right: Add '2550' to each side of the equation. -2550 + -3x + 2550 + x2 = 0 + 2550 Reorder the terms: -2550 + 2550 + -3x + x2 = 0 + 2550 Combine like terms: -2550 + 2550 = 0 0 + -3x + x2 = 0 + 2550 -3x + x2 = 0 + 2550 Combine like terms: 0 + 2550 = 2550 -3x + x2 = 2550 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 = 2550 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2550 + 2.25 Combine like terms: 2550 + 2.25 = 2552.25 2.25 + -3x + x2 = 2552.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2552.25 Calculate the square root of the right side: 50.519798099 Break this problem into two subproblems by setting (x + -1.5) equal to 50.519798099 and -50.519798099.Subproblem 1
x + -1.5 = 50.519798099 Simplifying x + -1.5 = 50.519798099 Reorder the terms: -1.5 + x = 50.519798099 Solving -1.5 + x = 50.519798099 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 = 50.519798099 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 50.519798099 + 1.5 x = 50.519798099 + 1.5 Combine like terms: 50.519798099 + 1.5 = 52.019798099 x = 52.019798099 Simplifying x = 52.019798099Subproblem 2
x + -1.5 = -50.519798099 Simplifying x + -1.5 = -50.519798099 Reorder the terms: -1.5 + x = -50.519798099 Solving -1.5 + x = -50.519798099 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 = -50.519798099 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -50.519798099 + 1.5 x = -50.519798099 + 1.5 Combine like terms: -50.519798099 + 1.5 = -49.019798099 x = -49.019798099 Simplifying x = -49.019798099Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.019798099, -49.019798099}
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