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Simplifying 5x2 + -12x + -1080 = 0 Reorder the terms: -1080 + -12x + 5x2 = 0 Solving -1080 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -216 + -2.4x + x2 = 0 Move the constant term to the right: Add '216' to each side of the equation. -216 + -2.4x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + -2.4x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + -2.4x + x2 = 0 + 216 -2.4x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 -2.4x + x2 = 216 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 216 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 216 + 1.44 Combine like terms: 216 + 1.44 = 217.44 1.44 + -2.4x + x2 = 217.44 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 217.44 Calculate the square root of the right side: 14.745846873 Break this problem into two subproblems by setting (x + -1.2) equal to 14.745846873 and -14.745846873.Subproblem 1
x + -1.2 = 14.745846873 Simplifying x + -1.2 = 14.745846873 Reorder the terms: -1.2 + x = 14.745846873 Solving -1.2 + x = 14.745846873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 14.745846873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 14.745846873 + 1.2 x = 14.745846873 + 1.2 Combine like terms: 14.745846873 + 1.2 = 15.945846873 x = 15.945846873 Simplifying x = 15.945846873Subproblem 2
x + -1.2 = -14.745846873 Simplifying x + -1.2 = -14.745846873 Reorder the terms: -1.2 + x = -14.745846873 Solving -1.2 + x = -14.745846873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -14.745846873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -14.745846873 + 1.2 x = -14.745846873 + 1.2 Combine like terms: -14.745846873 + 1.2 = -13.545846873 x = -13.545846873 Simplifying x = -13.545846873Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.945846873, -13.545846873}
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