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Simplifying 2x2 + 25x + -4.5 = 0 Reorder the terms: -4.5 + 25x + 2x2 = 0 Solving -4.5 + 25x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.25 + 12.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 12.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 12.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 12.5x + x2 = 0 + 2.25 12.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 12.5x + x2 = 2.25 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 2.25 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 2.25 + 39.0625 Combine like terms: 2.25 + 39.0625 = 41.3125 39.0625 + 12.5x + x2 = 41.3125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 41.3125 Calculate the square root of the right side: 6.427480066 Break this problem into two subproblems by setting (x + 6.25) equal to 6.427480066 and -6.427480066.Subproblem 1
x + 6.25 = 6.427480066 Simplifying x + 6.25 = 6.427480066 Reorder the terms: 6.25 + x = 6.427480066 Solving 6.25 + x = 6.427480066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 6.427480066 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.427480066 + -6.25 x = 6.427480066 + -6.25 Combine like terms: 6.427480066 + -6.25 = 0.177480066 x = 0.177480066 Simplifying x = 0.177480066Subproblem 2
x + 6.25 = -6.427480066 Simplifying x + 6.25 = -6.427480066 Reorder the terms: 6.25 + x = -6.427480066 Solving 6.25 + x = -6.427480066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -6.427480066 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.427480066 + -6.25 x = -6.427480066 + -6.25 Combine like terms: -6.427480066 + -6.25 = -12.677480066 x = -12.677480066 Simplifying x = -12.677480066Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177480066, -12.677480066}
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