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Simplifying x2 + -3x + -400 = 0 Reorder the terms: -400 + -3x + x2 = 0 Solving -400 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -3x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -3x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -3x + x2 = 0 + 400 -3x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -3x + x2 = 400 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 400 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 400 + 2.25 Combine like terms: 400 + 2.25 = 402.25 2.25 + -3x + x2 = 402.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 402.25 Calculate the square root of the right side: 20.05617112 Break this problem into two subproblems by setting (x + -1.5) equal to 20.05617112 and -20.05617112.Subproblem 1
x + -1.5 = 20.05617112 Simplifying x + -1.5 = 20.05617112 Reorder the terms: -1.5 + x = 20.05617112 Solving -1.5 + x = 20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 20.05617112 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 20.05617112 + 1.5 x = 20.05617112 + 1.5 Combine like terms: 20.05617112 + 1.5 = 21.55617112 x = 21.55617112 Simplifying x = 21.55617112Subproblem 2
x + -1.5 = -20.05617112 Simplifying x + -1.5 = -20.05617112 Reorder the terms: -1.5 + x = -20.05617112 Solving -1.5 + x = -20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -20.05617112 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -20.05617112 + 1.5 x = -20.05617112 + 1.5 Combine like terms: -20.05617112 + 1.5 = -18.55617112 x = -18.55617112 Simplifying x = -18.55617112Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.55617112, -18.55617112}
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