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Simplifying x2 + 8x + -300 = 2980 Reorder the terms: -300 + 8x + x2 = 2980 Solving -300 + 8x + x2 = 2980 Solving for variable 'x'. Reorder the terms: -300 + -2980 + 8x + x2 = 2980 + -2980 Combine like terms: -300 + -2980 = -3280 -3280 + 8x + x2 = 2980 + -2980 Combine like terms: 2980 + -2980 = 0 -3280 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3280' to each side of the equation. -3280 + 8x + 3280 + x2 = 0 + 3280 Reorder the terms: -3280 + 3280 + 8x + x2 = 0 + 3280 Combine like terms: -3280 + 3280 = 0 0 + 8x + x2 = 0 + 3280 8x + x2 = 0 + 3280 Combine like terms: 0 + 3280 = 3280 8x + x2 = 3280 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 = 3280 + 16 Reorder the terms: 16 + 8x + x2 = 3280 + 16 Combine like terms: 3280 + 16 = 3296 16 + 8x + x2 = 3296 Factor a perfect square on the left side: (x + 4)(x + 4) = 3296 Calculate the square root of the right side: 57.410800378 Break this problem into two subproblems by setting (x + 4) equal to 57.410800378 and -57.410800378.Subproblem 1
x + 4 = 57.410800378 Simplifying x + 4 = 57.410800378 Reorder the terms: 4 + x = 57.410800378 Solving 4 + x = 57.410800378 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 = 57.410800378 + -4 Combine like terms: 4 + -4 = 0 0 + x = 57.410800378 + -4 x = 57.410800378 + -4 Combine like terms: 57.410800378 + -4 = 53.410800378 x = 53.410800378 Simplifying x = 53.410800378Subproblem 2
x + 4 = -57.410800378 Simplifying x + 4 = -57.410800378 Reorder the terms: 4 + x = -57.410800378 Solving 4 + x = -57.410800378 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 = -57.410800378 + -4 Combine like terms: 4 + -4 = 0 0 + x = -57.410800378 + -4 x = -57.410800378 + -4 Combine like terms: -57.410800378 + -4 = -61.410800378 x = -61.410800378 Simplifying x = -61.410800378Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.410800378, -61.410800378}
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