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Simplifying 18000 + -10x + -0.2x2 = 0 Solving 18000 + -10x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -90000 + 50x + x2 = 0 Move the constant term to the right: Add '90000' to each side of the equation. -90000 + 50x + 90000 + x2 = 0 + 90000 Reorder the terms: -90000 + 90000 + 50x + x2 = 0 + 90000 Combine like terms: -90000 + 90000 = 0 0 + 50x + x2 = 0 + 90000 50x + x2 = 0 + 90000 Combine like terms: 0 + 90000 = 90000 50x + x2 = 90000 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 90000 + 625 Reorder the terms: 625 + 50x + x2 = 90000 + 625 Combine like terms: 90000 + 625 = 90625 625 + 50x + x2 = 90625 Factor a perfect square on the left side: (x + 25)(x + 25) = 90625 Calculate the square root of the right side: 301.03986447 Break this problem into two subproblems by setting (x + 25) equal to 301.03986447 and -301.03986447.Subproblem 1
x + 25 = 301.03986447 Simplifying x + 25 = 301.03986447 Reorder the terms: 25 + x = 301.03986447 Solving 25 + x = 301.03986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 301.03986447 + -25 Combine like terms: 25 + -25 = 0 0 + x = 301.03986447 + -25 x = 301.03986447 + -25 Combine like terms: 301.03986447 + -25 = 276.03986447 x = 276.03986447 Simplifying x = 276.03986447Subproblem 2
x + 25 = -301.03986447 Simplifying x + 25 = -301.03986447 Reorder the terms: 25 + x = -301.03986447 Solving 25 + x = -301.03986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -301.03986447 + -25 Combine like terms: 25 + -25 = 0 0 + x = -301.03986447 + -25 x = -301.03986447 + -25 Combine like terms: -301.03986447 + -25 = -326.03986447 x = -326.03986447 Simplifying x = -326.03986447Solution
The solution to the problem is based on the solutions from the subproblems. x = {276.03986447, -326.03986447}
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