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Simplifying 2x2 + 7x + -108 = 0 Reorder the terms: -108 + 7x + 2x2 = 0 Solving -108 + 7x + 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'. -54 + 3.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 3.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 3.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 3.5x + x2 = 0 + 54 3.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 3.5x + x2 = 54 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 54 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 54 + 3.0625 Combine like terms: 54 + 3.0625 = 57.0625 3.0625 + 3.5x + x2 = 57.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 57.0625 Calculate the square root of the right side: 7.553972465 Break this problem into two subproblems by setting (x + 1.75) equal to 7.553972465 and -7.553972465.Subproblem 1
x + 1.75 = 7.553972465 Simplifying x + 1.75 = 7.553972465 Reorder the terms: 1.75 + x = 7.553972465 Solving 1.75 + x = 7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 7.553972465 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 7.553972465 + -1.75 x = 7.553972465 + -1.75 Combine like terms: 7.553972465 + -1.75 = 5.803972465 x = 5.803972465 Simplifying x = 5.803972465Subproblem 2
x + 1.75 = -7.553972465 Simplifying x + 1.75 = -7.553972465 Reorder the terms: 1.75 + x = -7.553972465 Solving 1.75 + x = -7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -7.553972465 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -7.553972465 + -1.75 x = -7.553972465 + -1.75 Combine like terms: -7.553972465 + -1.75 = -9.303972465 x = -9.303972465 Simplifying x = -9.303972465Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.803972465, -9.303972465}
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