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Simplifying 2x2 + 1x + -52 = 0 Reorder the terms: -52 + 1x + 2x2 = 0 Solving -52 + 1x + 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'. -26 + 0.5x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 0.5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 0.5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 0.5x + x2 = 0 + 26 0.5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 0.5x + x2 = 26 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 26 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 26 + 0.0625 Combine like terms: 26 + 0.0625 = 26.0625 0.0625 + 0.5x + x2 = 26.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (x + 0.25) equal to 5.105144464 and -5.105144464.Subproblem 1
x + 0.25 = 5.105144464 Simplifying x + 0.25 = 5.105144464 Reorder the terms: 0.25 + x = 5.105144464 Solving 0.25 + x = 5.105144464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 5.105144464 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 5.105144464 + -0.25 x = 5.105144464 + -0.25 Combine like terms: 5.105144464 + -0.25 = 4.855144464 x = 4.855144464 Simplifying x = 4.855144464Subproblem 2
x + 0.25 = -5.105144464 Simplifying x + 0.25 = -5.105144464 Reorder the terms: 0.25 + x = -5.105144464 Solving 0.25 + x = -5.105144464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -5.105144464 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -5.105144464 + -0.25 x = -5.105144464 + -0.25 Combine like terms: -5.105144464 + -0.25 = -5.355144464 x = -5.355144464 Simplifying x = -5.355144464Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.855144464, -5.355144464}
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