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Simplifying 2x2 + -39x + -80 = 0 Reorder the terms: -80 + -39x + 2x2 = 0 Solving -80 + -39x + 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'. -40 + -19.5x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -19.5x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -19.5x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -19.5x + x2 = 0 + 40 -19.5x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -19.5x + x2 = 40 The x term is -19.5x. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5x + 95.0625 + x2 = 40 + 95.0625 Reorder the terms: 95.0625 + -19.5x + x2 = 40 + 95.0625 Combine like terms: 40 + 95.0625 = 135.0625 95.0625 + -19.5x + x2 = 135.0625 Factor a perfect square on the left side: (x + -9.75)(x + -9.75) = 135.0625 Calculate the square root of the right side: 11.621639299 Break this problem into two subproblems by setting (x + -9.75) equal to 11.621639299 and -11.621639299.Subproblem 1
x + -9.75 = 11.621639299 Simplifying x + -9.75 = 11.621639299 Reorder the terms: -9.75 + x = 11.621639299 Solving -9.75 + x = 11.621639299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = 11.621639299 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = 11.621639299 + 9.75 x = 11.621639299 + 9.75 Combine like terms: 11.621639299 + 9.75 = 21.371639299 x = 21.371639299 Simplifying x = 21.371639299Subproblem 2
x + -9.75 = -11.621639299 Simplifying x + -9.75 = -11.621639299 Reorder the terms: -9.75 + x = -11.621639299 Solving -9.75 + x = -11.621639299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = -11.621639299 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = -11.621639299 + 9.75 x = -11.621639299 + 9.75 Combine like terms: -11.621639299 + 9.75 = -1.871639299 x = -1.871639299 Simplifying x = -1.871639299Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.371639299, -1.871639299}
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