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Simplifying 2x2 + 17x + -7.5 = 0 Reorder the terms: -7.5 + 17x + 2x2 = 0 Solving -7.5 + 17x + 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'. -3.75 + 8.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 8.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 8.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 8.5x + x2 = 0 + 3.75 8.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 8.5x + x2 = 3.75 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 3.75 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 3.75 + 18.0625 Combine like terms: 3.75 + 18.0625 = 21.8125 18.0625 + 8.5x + x2 = 21.8125 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 21.8125 Calculate the square root of the right side: 4.670385423 Break this problem into two subproblems by setting (x + 4.25) equal to 4.670385423 and -4.670385423.Subproblem 1
x + 4.25 = 4.670385423 Simplifying x + 4.25 = 4.670385423 Reorder the terms: 4.25 + x = 4.670385423 Solving 4.25 + x = 4.670385423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.670385423 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.670385423 + -4.25 x = 4.670385423 + -4.25 Combine like terms: 4.670385423 + -4.25 = 0.420385423 x = 0.420385423 Simplifying x = 0.420385423Subproblem 2
x + 4.25 = -4.670385423 Simplifying x + 4.25 = -4.670385423 Reorder the terms: 4.25 + x = -4.670385423 Solving 4.25 + x = -4.670385423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.670385423 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.670385423 + -4.25 x = -4.670385423 + -4.25 Combine like terms: -4.670385423 + -4.25 = -8.920385423 x = -8.920385423 Simplifying x = -8.920385423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.420385423, -8.920385423}
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