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Simplifying 2x2 + 5x + -384 = 0 Reorder the terms: -384 + 5x + 2x2 = 0 Solving -384 + 5x + 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 + 2.5x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 2.5x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 2.5x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 2.5x + x2 = 0 + 192 2.5x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 2.5x + x2 = 192 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 192 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 192 + 1.5625 Combine like terms: 192 + 1.5625 = 193.5625 1.5625 + 2.5x + x2 = 193.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 193.5625 Calculate the square root of the right side: 13.912674078 Break this problem into two subproblems by setting (x + 1.25) equal to 13.912674078 and -13.912674078.Subproblem 1
x + 1.25 = 13.912674078 Simplifying x + 1.25 = 13.912674078 Reorder the terms: 1.25 + x = 13.912674078 Solving 1.25 + x = 13.912674078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 13.912674078 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 13.912674078 + -1.25 x = 13.912674078 + -1.25 Combine like terms: 13.912674078 + -1.25 = 12.662674078 x = 12.662674078 Simplifying x = 12.662674078Subproblem 2
x + 1.25 = -13.912674078 Simplifying x + 1.25 = -13.912674078 Reorder the terms: 1.25 + x = -13.912674078 Solving 1.25 + x = -13.912674078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -13.912674078 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -13.912674078 + -1.25 x = -13.912674078 + -1.25 Combine like terms: -13.912674078 + -1.25 = -15.162674078 x = -15.162674078 Simplifying x = -15.162674078Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.662674078, -15.162674078}
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