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Simplifying 2x2 + -24x + 53 = 0 Reorder the terms: 53 + -24x + 2x2 = 0 Solving 53 + -24x + 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'. 26.5 + -12x + x2 = 0 Move the constant term to the right: Add '-26.5' to each side of the equation. 26.5 + -12x + -26.5 + x2 = 0 + -26.5 Reorder the terms: 26.5 + -26.5 + -12x + x2 = 0 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + -12x + x2 = 0 + -26.5 -12x + x2 = 0 + -26.5 Combine like terms: 0 + -26.5 = -26.5 -12x + x2 = -26.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -26.5 + 36 Reorder the terms: 36 + -12x + x2 = -26.5 + 36 Combine like terms: -26.5 + 36 = 9.5 36 + -12x + x2 = 9.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -6) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -6 = 3.082207001 Simplifying x + -6 = 3.082207001 Reorder the terms: -6 + x = 3.082207001 Solving -6 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.082207001 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.082207001 + 6 x = 3.082207001 + 6 Combine like terms: 3.082207001 + 6 = 9.082207001 x = 9.082207001 Simplifying x = 9.082207001Subproblem 2
x + -6 = -3.082207001 Simplifying x + -6 = -3.082207001 Reorder the terms: -6 + x = -3.082207001 Solving -6 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.082207001 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.082207001 + 6 x = -3.082207001 + 6 Combine like terms: -3.082207001 + 6 = 2.917792999 x = 2.917792999 Simplifying x = 2.917792999Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.082207001, 2.917792999}
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