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Simplifying x2 + 8x + -300 = 0 Reorder the terms: -300 + 8x + x2 = 0 Solving -300 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 8x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 8x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 8x + x2 = 0 + 300 8x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 8x + x2 = 300 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 = 300 + 16 Reorder the terms: 16 + 8x + x2 = 300 + 16 Combine like terms: 300 + 16 = 316 16 + 8x + x2 = 316 Factor a perfect square on the left side: (x + 4)(x + 4) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (x + 4) equal to 17.776388835 and -17.776388835.Subproblem 1
x + 4 = 17.776388835 Simplifying x + 4 = 17.776388835 Reorder the terms: 4 + x = 17.776388835 Solving 4 + x = 17.776388835 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 = 17.776388835 + -4 Combine like terms: 4 + -4 = 0 0 + x = 17.776388835 + -4 x = 17.776388835 + -4 Combine like terms: 17.776388835 + -4 = 13.776388835 x = 13.776388835 Simplifying x = 13.776388835Subproblem 2
x + 4 = -17.776388835 Simplifying x + 4 = -17.776388835 Reorder the terms: 4 + x = -17.776388835 Solving 4 + x = -17.776388835 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 = -17.776388835 + -4 Combine like terms: 4 + -4 = 0 0 + x = -17.776388835 + -4 x = -17.776388835 + -4 Combine like terms: -17.776388835 + -4 = -21.776388835 x = -21.776388835 Simplifying x = -21.776388835Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.776388835, -21.776388835}
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