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Simplifying 2x2 + -5x + -78 = 0 Reorder the terms: -78 + -5x + 2x2 = 0 Solving -78 + -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'. -39 + -2.5x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -2.5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -2.5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -2.5x + x2 = 0 + 39 -2.5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -2.5x + x2 = 39 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 = 39 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 39 + 1.5625 Combine like terms: 39 + 1.5625 = 40.5625 1.5625 + -2.5x + x2 = 40.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 40.5625 Calculate the square root of the right side: 6.368869601 Break this problem into two subproblems by setting (x + -1.25) equal to 6.368869601 and -6.368869601.Subproblem 1
x + -1.25 = 6.368869601 Simplifying x + -1.25 = 6.368869601 Reorder the terms: -1.25 + x = 6.368869601 Solving -1.25 + x = 6.368869601 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 = 6.368869601 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.368869601 + 1.25 x = 6.368869601 + 1.25 Combine like terms: 6.368869601 + 1.25 = 7.618869601 x = 7.618869601 Simplifying x = 7.618869601Subproblem 2
x + -1.25 = -6.368869601 Simplifying x + -1.25 = -6.368869601 Reorder the terms: -1.25 + x = -6.368869601 Solving -1.25 + x = -6.368869601 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 = -6.368869601 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.368869601 + 1.25 x = -6.368869601 + 1.25 Combine like terms: -6.368869601 + 1.25 = -5.118869601 x = -5.118869601 Simplifying x = -5.118869601Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.618869601, -5.118869601}
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