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Simplifying x2 + -8x + -3000 = 0 Reorder the terms: -3000 + -8x + x2 = 0 Solving -3000 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + -8x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + -8x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + -8x + x2 = 0 + 3000 -8x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 -8x + x2 = 3000 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 = 3000 + 16 Reorder the terms: 16 + -8x + x2 = 3000 + 16 Combine like terms: 3000 + 16 = 3016 16 + -8x + x2 = 3016 Factor a perfect square on the left side: (x + -4)(x + -4) = 3016 Calculate the square root of the right side: 54.918120871 Break this problem into two subproblems by setting (x + -4) equal to 54.918120871 and -54.918120871.Subproblem 1
x + -4 = 54.918120871 Simplifying x + -4 = 54.918120871 Reorder the terms: -4 + x = 54.918120871 Solving -4 + x = 54.918120871 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 = 54.918120871 + 4 Combine like terms: -4 + 4 = 0 0 + x = 54.918120871 + 4 x = 54.918120871 + 4 Combine like terms: 54.918120871 + 4 = 58.918120871 x = 58.918120871 Simplifying x = 58.918120871Subproblem 2
x + -4 = -54.918120871 Simplifying x + -4 = -54.918120871 Reorder the terms: -4 + x = -54.918120871 Solving -4 + x = -54.918120871 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 = -54.918120871 + 4 Combine like terms: -4 + 4 = 0 0 + x = -54.918120871 + 4 x = -54.918120871 + 4 Combine like terms: -54.918120871 + 4 = -50.918120871 x = -50.918120871 Simplifying x = -50.918120871Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.918120871, -50.918120871}
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