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Simplifying x2 + -2x + -4 = 2.25x + -5 Reorder the terms: -4 + -2x + x2 = 2.25x + -5 Reorder the terms: -4 + -2x + x2 = -5 + 2.25x Solving -4 + -2x + x2 = -5 + 2.25x Solving for variable 'x'. Reorder the terms: -4 + 5 + -2x + -2.25x + x2 = -5 + 2.25x + 5 + -2.25x Combine like terms: -4 + 5 = 1 1 + -2x + -2.25x + x2 = -5 + 2.25x + 5 + -2.25x Combine like terms: -2x + -2.25x = -4.25x 1 + -4.25x + x2 = -5 + 2.25x + 5 + -2.25x Reorder the terms: 1 + -4.25x + x2 = -5 + 5 + 2.25x + -2.25x Combine like terms: -5 + 5 = 0 1 + -4.25x + x2 = 0 + 2.25x + -2.25x 1 + -4.25x + x2 = 2.25x + -2.25x Combine like terms: 2.25x + -2.25x = 0.00 1 + -4.25x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.25x + -1 + x2 = 0.00 + -1 Reorder the terms: 1 + -1 + -4.25x + x2 = 0.00 + -1 Combine like terms: 1 + -1 = 0 0 + -4.25x + x2 = 0.00 + -1 -4.25x + x2 = 0.00 + -1 Combine like terms: 0.00 + -1 = -1 -4.25x + x2 = -1 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -1 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -1 + 4.515625 Combine like terms: -1 + 4.515625 = 3.515625 4.515625 + -4.25x + x2 = 3.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 3.515625 Calculate the square root of the right side: 1.875 Break this problem into two subproblems by setting (x + -2.125) equal to 1.875 and -1.875.Subproblem 1
x + -2.125 = 1.875 Simplifying x + -2.125 = 1.875 Reorder the terms: -2.125 + x = 1.875 Solving -2.125 + x = 1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.875 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.875 + 2.125 x = 1.875 + 2.125 Combine like terms: 1.875 + 2.125 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -2.125 = -1.875 Simplifying x + -2.125 = -1.875 Reorder the terms: -2.125 + x = -1.875 Solving -2.125 + x = -1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.875 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.875 + 2.125 x = -1.875 + 2.125 Combine like terms: -1.875 + 2.125 = 0.25 x = 0.25 Simplifying x = 0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 0.25}
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