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Simplifying 2x2 + -8x + 0.5x + -2 = 0 Reorder the terms: -2 + -8x + 0.5x + 2x2 = 0 Combine like terms: -8x + 0.5x = -7.5x -2 + -7.5x + 2x2 = 0 Solving -2 + -7.5x + 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'. -1 + -3.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.75x + x2 = 0 + 1 -3.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.75x + x2 = 1 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 1 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 1 + 3.515625 Combine like terms: 1 + 3.515625 = 4.515625 3.515625 + -3.75x + x2 = 4.515625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 4.515625 Calculate the square root of the right side: 2.125 Break this problem into two subproblems by setting (x + -1.875) equal to 2.125 and -2.125.Subproblem 1
x + -1.875 = 2.125 Simplifying x + -1.875 = 2.125 Reorder the terms: -1.875 + x = 2.125 Solving -1.875 + x = 2.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.125 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.125 + 1.875 x = 2.125 + 1.875 Combine like terms: 2.125 + 1.875 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -1.875 = -2.125 Simplifying x + -1.875 = -2.125 Reorder the terms: -1.875 + x = -2.125 Solving -1.875 + x = -2.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.125 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.125 + 1.875 x = -2.125 + 1.875 Combine like terms: -2.125 + 1.875 = -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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