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Simplifying x2 + 8x + -77 = 0 Reorder the terms: -77 + 8x + x2 = 0 Solving -77 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 8x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 8x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 8x + x2 = 0 + 77 8x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 8x + x2 = 77 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 77 + 16 Reorder the terms: 16 + 8x + x2 = 77 + 16 Combine like terms: 77 + 16 = 93 16 + 8x + x2 = 93 Factor a perfect square on the left side: (x + 4)(x + 4) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (x + 4) equal to 9.643650761 and -9.643650761.Subproblem 1
x + 4 = 9.643650761 Simplifying x + 4 = 9.643650761 Reorder the terms: 4 + x = 9.643650761 Solving 4 + x = 9.643650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 9.643650761 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.643650761 + -4 x = 9.643650761 + -4 Combine like terms: 9.643650761 + -4 = 5.643650761 x = 5.643650761 Simplifying x = 5.643650761Subproblem 2
x + 4 = -9.643650761 Simplifying x + 4 = -9.643650761 Reorder the terms: 4 + x = -9.643650761 Solving 4 + x = -9.643650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -9.643650761 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.643650761 + -4 x = -9.643650761 + -4 Combine like terms: -9.643650761 + -4 = -13.643650761 x = -13.643650761 Simplifying x = -13.643650761Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.643650761, -13.643650761}
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