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Simplifying x2 + 8x + -300 = 2400 Reorder the terms: -300 + 8x + x2 = 2400 Solving -300 + 8x + x2 = 2400 Solving for variable 'x'. Reorder the terms: -300 + -2400 + 8x + x2 = 2400 + -2400 Combine like terms: -300 + -2400 = -2700 -2700 + 8x + x2 = 2400 + -2400 Combine like terms: 2400 + -2400 = 0 -2700 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + 8x + 2700 + x2 = 0 + 2700 Reorder the terms: -2700 + 2700 + 8x + x2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + 8x + x2 = 0 + 2700 8x + x2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 8x + x2 = 2700 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 = 2700 + 16 Reorder the terms: 16 + 8x + x2 = 2700 + 16 Combine like terms: 2700 + 16 = 2716 16 + 8x + x2 = 2716 Factor a perfect square on the left side: (x + 4)(x + 4) = 2716 Calculate the square root of the right side: 52.115256883 Break this problem into two subproblems by setting (x + 4) equal to 52.115256883 and -52.115256883.Subproblem 1
x + 4 = 52.115256883 Simplifying x + 4 = 52.115256883 Reorder the terms: 4 + x = 52.115256883 Solving 4 + x = 52.115256883 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 = 52.115256883 + -4 Combine like terms: 4 + -4 = 0 0 + x = 52.115256883 + -4 x = 52.115256883 + -4 Combine like terms: 52.115256883 + -4 = 48.115256883 x = 48.115256883 Simplifying x = 48.115256883Subproblem 2
x + 4 = -52.115256883 Simplifying x + 4 = -52.115256883 Reorder the terms: 4 + x = -52.115256883 Solving 4 + x = -52.115256883 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 = -52.115256883 + -4 Combine like terms: 4 + -4 = 0 0 + x = -52.115256883 + -4 x = -52.115256883 + -4 Combine like terms: -52.115256883 + -4 = -56.115256883 x = -56.115256883 Simplifying x = -56.115256883Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.115256883, -56.115256883}
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