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Simplifying 3x2 + -30x + -4000 = 0 Reorder the terms: -4000 + -30x + 3x2 = 0 Solving -4000 + -30x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1333.333333 + -10x + x2 = 0 Move the constant term to the right: Add '1333.333333' to each side of the equation. -1333.333333 + -10x + 1333.333333 + x2 = 0 + 1333.333333 Reorder the terms: -1333.333333 + 1333.333333 + -10x + x2 = 0 + 1333.333333 Combine like terms: -1333.333333 + 1333.333333 = 0.000000 0.000000 + -10x + x2 = 0 + 1333.333333 -10x + x2 = 0 + 1333.333333 Combine like terms: 0 + 1333.333333 = 1333.333333 -10x + x2 = 1333.333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 1333.333333 + 25 Reorder the terms: 25 + -10x + x2 = 1333.333333 + 25 Combine like terms: 1333.333333 + 25 = 1358.333333 25 + -10x + x2 = 1358.333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 1358.333333 Calculate the square root of the right side: 36.855573975 Break this problem into two subproblems by setting (x + -5) equal to 36.855573975 and -36.855573975.Subproblem 1
x + -5 = 36.855573975 Simplifying x + -5 = 36.855573975 Reorder the terms: -5 + x = 36.855573975 Solving -5 + x = 36.855573975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 36.855573975 + 5 Combine like terms: -5 + 5 = 0 0 + x = 36.855573975 + 5 x = 36.855573975 + 5 Combine like terms: 36.855573975 + 5 = 41.855573975 x = 41.855573975 Simplifying x = 41.855573975Subproblem 2
x + -5 = -36.855573975 Simplifying x + -5 = -36.855573975 Reorder the terms: -5 + x = -36.855573975 Solving -5 + x = -36.855573975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -36.855573975 + 5 Combine like terms: -5 + 5 = 0 0 + x = -36.855573975 + 5 x = -36.855573975 + 5 Combine like terms: -36.855573975 + 5 = -31.855573975 x = -31.855573975 Simplifying x = -31.855573975Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.855573975, -31.855573975}
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