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Simplifying -3x2 + 60x + 4000 = 0 Reorder the terms: 4000 + 60x + -3x2 = 0 Solving 4000 + 60x + -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 + -20x + x2 = 0 Move the constant term to the right: Add '1333.333333' to each side of the equation. -1333.333333 + -20x + 1333.333333 + x2 = 0 + 1333.333333 Reorder the terms: -1333.333333 + 1333.333333 + -20x + x2 = 0 + 1333.333333 Combine like terms: -1333.333333 + 1333.333333 = 0.000000 0.000000 + -20x + x2 = 0 + 1333.333333 -20x + x2 = 0 + 1333.333333 Combine like terms: 0 + 1333.333333 = 1333.333333 -20x + x2 = 1333.333333 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 1333.333333 + 100 Reorder the terms: 100 + -20x + x2 = 1333.333333 + 100 Combine like terms: 1333.333333 + 100 = 1433.333333 100 + -20x + x2 = 1433.333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 1433.333333 Calculate the square root of the right side: 37.859388968 Break this problem into two subproblems by setting (x + -10) equal to 37.859388968 and -37.859388968.Subproblem 1
x + -10 = 37.859388968 Simplifying x + -10 = 37.859388968 Reorder the terms: -10 + x = 37.859388968 Solving -10 + x = 37.859388968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 37.859388968 + 10 Combine like terms: -10 + 10 = 0 0 + x = 37.859388968 + 10 x = 37.859388968 + 10 Combine like terms: 37.859388968 + 10 = 47.859388968 x = 47.859388968 Simplifying x = 47.859388968Subproblem 2
x + -10 = -37.859388968 Simplifying x + -10 = -37.859388968 Reorder the terms: -10 + x = -37.859388968 Solving -10 + x = -37.859388968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -37.859388968 + 10 Combine like terms: -10 + 10 = 0 0 + x = -37.859388968 + 10 x = -37.859388968 + 10 Combine like terms: -37.859388968 + 10 = -27.859388968 x = -27.859388968 Simplifying x = -27.859388968Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.859388968, -27.859388968}
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