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Simplifying 2x2 + -41x + 78 = 0 Reorder the terms: 78 + -41x + 2x2 = 0 Solving 78 + -41x + 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'. 39 + -20.5x + x2 = 0 Move the constant term to the right: Add '-39' to each side of the equation. 39 + -20.5x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -20.5x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -20.5x + x2 = 0 + -39 -20.5x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -20.5x + x2 = -39 The x term is -20.5x. Take half its coefficient (-10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. -20.5x + 105.0625 + x2 = -39 + 105.0625 Reorder the terms: 105.0625 + -20.5x + x2 = -39 + 105.0625 Combine like terms: -39 + 105.0625 = 66.0625 105.0625 + -20.5x + x2 = 66.0625 Factor a perfect square on the left side: (x + -10.25)(x + -10.25) = 66.0625 Calculate the square root of the right side: 8.127884104 Break this problem into two subproblems by setting (x + -10.25) equal to 8.127884104 and -8.127884104.Subproblem 1
x + -10.25 = 8.127884104 Simplifying x + -10.25 = 8.127884104 Reorder the terms: -10.25 + x = 8.127884104 Solving -10.25 + x = 8.127884104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = 8.127884104 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = 8.127884104 + 10.25 x = 8.127884104 + 10.25 Combine like terms: 8.127884104 + 10.25 = 18.377884104 x = 18.377884104 Simplifying x = 18.377884104Subproblem 2
x + -10.25 = -8.127884104 Simplifying x + -10.25 = -8.127884104 Reorder the terms: -10.25 + x = -8.127884104 Solving -10.25 + x = -8.127884104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = -8.127884104 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = -8.127884104 + 10.25 x = -8.127884104 + 10.25 Combine like terms: -8.127884104 + 10.25 = 2.122115896 x = 2.122115896 Simplifying x = 2.122115896Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.377884104, 2.122115896}
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