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Simplifying 4x2 + 37x + -4000 = 0 Reorder the terms: -4000 + 37x + 4x2 = 0 Solving -4000 + 37x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1000 + 9.25x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 9.25x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 9.25x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 9.25x + x2 = 0 + 1000 9.25x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 9.25x + x2 = 1000 The x term is 9.25x. Take half its coefficient (4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. 9.25x + 21.390625 + x2 = 1000 + 21.390625 Reorder the terms: 21.390625 + 9.25x + x2 = 1000 + 21.390625 Combine like terms: 1000 + 21.390625 = 1021.390625 21.390625 + 9.25x + x2 = 1021.390625 Factor a perfect square on the left side: (x + 4.625)(x + 4.625) = 1021.390625 Calculate the square root of the right side: 31.959202509 Break this problem into two subproblems by setting (x + 4.625) equal to 31.959202509 and -31.959202509.Subproblem 1
x + 4.625 = 31.959202509 Simplifying x + 4.625 = 31.959202509 Reorder the terms: 4.625 + x = 31.959202509 Solving 4.625 + x = 31.959202509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + x = 31.959202509 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = 31.959202509 + -4.625 x = 31.959202509 + -4.625 Combine like terms: 31.959202509 + -4.625 = 27.334202509 x = 27.334202509 Simplifying x = 27.334202509Subproblem 2
x + 4.625 = -31.959202509 Simplifying x + 4.625 = -31.959202509 Reorder the terms: 4.625 + x = -31.959202509 Solving 4.625 + x = -31.959202509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + x = -31.959202509 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + x = -31.959202509 + -4.625 x = -31.959202509 + -4.625 Combine like terms: -31.959202509 + -4.625 = -36.584202509 x = -36.584202509 Simplifying x = -36.584202509Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.334202509, -36.584202509}
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