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Simplifying x = 0.25x2 + -0.125x + -12.25 Reorder the terms: x = -12.25 + -0.125x + 0.25x2 Solving x = -12.25 + -0.125x + 0.25x2 Solving for variable 'x'. Reorder the terms: 12.25 + x + 0.125x + -0.25x2 = -12.25 + -0.125x + 0.25x2 + 12.25 + 0.125x + -0.25x2 Combine like terms: x + 0.125x = 1.125x 12.25 + 1.125x + -0.25x2 = -12.25 + -0.125x + 0.25x2 + 12.25 + 0.125x + -0.25x2 Reorder the terms: 12.25 + 1.125x + -0.25x2 = -12.25 + 12.25 + -0.125x + 0.125x + 0.25x2 + -0.25x2 Combine like terms: -12.25 + 12.25 = 0.00 12.25 + 1.125x + -0.25x2 = 0.00 + -0.125x + 0.125x + 0.25x2 + -0.25x2 12.25 + 1.125x + -0.25x2 = -0.125x + 0.125x + 0.25x2 + -0.25x2 Combine like terms: -0.125x + 0.125x = 0.000 12.25 + 1.125x + -0.25x2 = 0.000 + 0.25x2 + -0.25x2 12.25 + 1.125x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 12.25 + 1.125x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -49 + -4.5x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -4.5x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -4.5x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -4.5x + x2 = 0 + 49 -4.5x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -4.5x + x2 = 49 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 49 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 49 + 5.0625 Combine like terms: 49 + 5.0625 = 54.0625 5.0625 + -4.5x + x2 = 54.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 54.0625 Calculate the square root of the right side: 7.352720585 Break this problem into two subproblems by setting (x + -2.25) equal to 7.352720585 and -7.352720585.Subproblem 1
x + -2.25 = 7.352720585 Simplifying x + -2.25 = 7.352720585 Reorder the terms: -2.25 + x = 7.352720585 Solving -2.25 + x = 7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 7.352720585 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.352720585 + 2.25 x = 7.352720585 + 2.25 Combine like terms: 7.352720585 + 2.25 = 9.602720585 x = 9.602720585 Simplifying x = 9.602720585Subproblem 2
x + -2.25 = -7.352720585 Simplifying x + -2.25 = -7.352720585 Reorder the terms: -2.25 + x = -7.352720585 Solving -2.25 + x = -7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -7.352720585 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.352720585 + 2.25 x = -7.352720585 + 2.25 Combine like terms: -7.352720585 + 2.25 = -5.102720585 x = -5.102720585 Simplifying x = -5.102720585Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.602720585, -5.102720585}
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