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Simplifying 4x2 + 54x + 119 = 0 Reorder the terms: 119 + 54x + 4x2 = 0 Solving 119 + 54x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 29.75 + 13.5x + x2 = 0 Move the constant term to the right: Add '-29.75' to each side of the equation. 29.75 + 13.5x + -29.75 + x2 = 0 + -29.75 Reorder the terms: 29.75 + -29.75 + 13.5x + x2 = 0 + -29.75 Combine like terms: 29.75 + -29.75 = 0.00 0.00 + 13.5x + x2 = 0 + -29.75 13.5x + x2 = 0 + -29.75 Combine like terms: 0 + -29.75 = -29.75 13.5x + x2 = -29.75 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = -29.75 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = -29.75 + 45.5625 Combine like terms: -29.75 + 45.5625 = 15.8125 45.5625 + 13.5x + x2 = 15.8125 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 15.8125 Calculate the square root of the right side: 3.97649343 Break this problem into two subproblems by setting (x + 6.75) equal to 3.97649343 and -3.97649343.Subproblem 1
x + 6.75 = 3.97649343 Simplifying x + 6.75 = 3.97649343 Reorder the terms: 6.75 + x = 3.97649343 Solving 6.75 + x = 3.97649343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 3.97649343 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 3.97649343 + -6.75 x = 3.97649343 + -6.75 Combine like terms: 3.97649343 + -6.75 = -2.77350657 x = -2.77350657 Simplifying x = -2.77350657Subproblem 2
x + 6.75 = -3.97649343 Simplifying x + 6.75 = -3.97649343 Reorder the terms: 6.75 + x = -3.97649343 Solving 6.75 + x = -3.97649343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -3.97649343 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -3.97649343 + -6.75 x = -3.97649343 + -6.75 Combine like terms: -3.97649343 + -6.75 = -10.72649343 x = -10.72649343 Simplifying x = -10.72649343Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.77350657, -10.72649343}
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