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Simplifying 2x2 + -39x + 72 = 0 Reorder the terms: 72 + -39x + 2x2 = 0 Solving 72 + -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'. 36 + -19.5x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -19.5x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -19.5x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -19.5x + x2 = 0 + -36 -19.5x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -19.5x + x2 = -36 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 = -36 + 95.0625 Reorder the terms: 95.0625 + -19.5x + x2 = -36 + 95.0625 Combine like terms: -36 + 95.0625 = 59.0625 95.0625 + -19.5x + x2 = 59.0625 Factor a perfect square on the left side: (x + -9.75)(x + -9.75) = 59.0625 Calculate the square root of the right side: 7.685213074 Break this problem into two subproblems by setting (x + -9.75) equal to 7.685213074 and -7.685213074.Subproblem 1
x + -9.75 = 7.685213074 Simplifying x + -9.75 = 7.685213074 Reorder the terms: -9.75 + x = 7.685213074 Solving -9.75 + x = 7.685213074 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 = 7.685213074 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = 7.685213074 + 9.75 x = 7.685213074 + 9.75 Combine like terms: 7.685213074 + 9.75 = 17.435213074 x = 17.435213074 Simplifying x = 17.435213074Subproblem 2
x + -9.75 = -7.685213074 Simplifying x + -9.75 = -7.685213074 Reorder the terms: -9.75 + x = -7.685213074 Solving -9.75 + x = -7.685213074 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 = -7.685213074 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = -7.685213074 + 9.75 x = -7.685213074 + 9.75 Combine like terms: -7.685213074 + 9.75 = 2.064786926 x = 2.064786926 Simplifying x = 2.064786926Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.435213074, 2.064786926}
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