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Simplifying 0.5x2 + 40x + -6000 = 0 Reorder the terms: -6000 + 40x + 0.5x2 = 0 Solving -6000 + 40x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -12000 + 80x + x2 = 0 Move the constant term to the right: Add '12000' to each side of the equation. -12000 + 80x + 12000 + x2 = 0 + 12000 Reorder the terms: -12000 + 12000 + 80x + x2 = 0 + 12000 Combine like terms: -12000 + 12000 = 0 0 + 80x + x2 = 0 + 12000 80x + x2 = 0 + 12000 Combine like terms: 0 + 12000 = 12000 80x + x2 = 12000 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 12000 + 1600 Reorder the terms: 1600 + 80x + x2 = 12000 + 1600 Combine like terms: 12000 + 1600 = 13600 1600 + 80x + x2 = 13600 Factor a perfect square on the left side: (x + 40)(x + 40) = 13600 Calculate the square root of the right side: 116.619037897 Break this problem into two subproblems by setting (x + 40) equal to 116.619037897 and -116.619037897.Subproblem 1
x + 40 = 116.619037897 Simplifying x + 40 = 116.619037897 Reorder the terms: 40 + x = 116.619037897 Solving 40 + x = 116.619037897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 116.619037897 + -40 Combine like terms: 40 + -40 = 0 0 + x = 116.619037897 + -40 x = 116.619037897 + -40 Combine like terms: 116.619037897 + -40 = 76.619037897 x = 76.619037897 Simplifying x = 76.619037897Subproblem 2
x + 40 = -116.619037897 Simplifying x + 40 = -116.619037897 Reorder the terms: 40 + x = -116.619037897 Solving 40 + x = -116.619037897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -116.619037897 + -40 Combine like terms: 40 + -40 = 0 0 + x = -116.619037897 + -40 x = -116.619037897 + -40 Combine like terms: -116.619037897 + -40 = -156.619037897 x = -156.619037897 Simplifying x = -156.619037897Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.619037897, -156.619037897}
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