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Simplifying 2x2 + -12x + -75 = 0 Reorder the terms: -75 + -12x + 2x2 = 0 Solving -75 + -12x + 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'. -37.5 + -6x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + -6x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -6x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -6x + x2 = 0 + 37.5 -6x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -6x + x2 = 37.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 37.5 + 9 Reorder the terms: 9 + -6x + x2 = 37.5 + 9 Combine like terms: 37.5 + 9 = 46.5 9 + -6x + x2 = 46.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 46.5 Calculate the square root of the right side: 6.819090848 Break this problem into two subproblems by setting (x + -3) equal to 6.819090848 and -6.819090848.Subproblem 1
x + -3 = 6.819090848 Simplifying x + -3 = 6.819090848 Reorder the terms: -3 + x = 6.819090848 Solving -3 + x = 6.819090848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.819090848 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.819090848 + 3 x = 6.819090848 + 3 Combine like terms: 6.819090848 + 3 = 9.819090848 x = 9.819090848 Simplifying x = 9.819090848Subproblem 2
x + -3 = -6.819090848 Simplifying x + -3 = -6.819090848 Reorder the terms: -3 + x = -6.819090848 Solving -3 + x = -6.819090848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.819090848 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.819090848 + 3 x = -6.819090848 + 3 Combine like terms: -6.819090848 + 3 = -3.819090848 x = -3.819090848 Simplifying x = -3.819090848Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.819090848, -3.819090848}
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