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Simplifying 2x2 + 7x + -384 = 0 Reorder the terms: -384 + 7x + 2x2 = 0 Solving -384 + 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'. -192 + 3.5x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 3.5x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 3.5x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 3.5x + x2 = 0 + 192 3.5x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 3.5x + x2 = 192 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 = 192 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 192 + 3.0625 Combine like terms: 192 + 3.0625 = 195.0625 3.0625 + 3.5x + x2 = 195.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 195.0625 Calculate the square root of the right side: 13.966477723 Break this problem into two subproblems by setting (x + 1.75) equal to 13.966477723 and -13.966477723.Subproblem 1
x + 1.75 = 13.966477723 Simplifying x + 1.75 = 13.966477723 Reorder the terms: 1.75 + x = 13.966477723 Solving 1.75 + x = 13.966477723 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 = 13.966477723 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 13.966477723 + -1.75 x = 13.966477723 + -1.75 Combine like terms: 13.966477723 + -1.75 = 12.216477723 x = 12.216477723 Simplifying x = 12.216477723Subproblem 2
x + 1.75 = -13.966477723 Simplifying x + 1.75 = -13.966477723 Reorder the terms: 1.75 + x = -13.966477723 Solving 1.75 + x = -13.966477723 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 = -13.966477723 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -13.966477723 + -1.75 x = -13.966477723 + -1.75 Combine like terms: -13.966477723 + -1.75 = -15.716477723 x = -15.716477723 Simplifying x = -15.716477723Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.216477723, -15.716477723}
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