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Simplifying x2 + -40x + -21000 = 0 Reorder the terms: -21000 + -40x + x2 = 0 Solving -21000 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21000' to each side of the equation. -21000 + -40x + 21000 + x2 = 0 + 21000 Reorder the terms: -21000 + 21000 + -40x + x2 = 0 + 21000 Combine like terms: -21000 + 21000 = 0 0 + -40x + x2 = 0 + 21000 -40x + x2 = 0 + 21000 Combine like terms: 0 + 21000 = 21000 -40x + x2 = 21000 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 21000 + 400 Reorder the terms: 400 + -40x + x2 = 21000 + 400 Combine like terms: 21000 + 400 = 21400 400 + -40x + x2 = 21400 Factor a perfect square on the left side: (x + -20)(x + -20) = 21400 Calculate the square root of the right side: 146.287388383 Break this problem into two subproblems by setting (x + -20) equal to 146.287388383 and -146.287388383.Subproblem 1
x + -20 = 146.287388383 Simplifying x + -20 = 146.287388383 Reorder the terms: -20 + x = 146.287388383 Solving -20 + x = 146.287388383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 146.287388383 + 20 Combine like terms: -20 + 20 = 0 0 + x = 146.287388383 + 20 x = 146.287388383 + 20 Combine like terms: 146.287388383 + 20 = 166.287388383 x = 166.287388383 Simplifying x = 166.287388383Subproblem 2
x + -20 = -146.287388383 Simplifying x + -20 = -146.287388383 Reorder the terms: -20 + x = -146.287388383 Solving -20 + x = -146.287388383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -146.287388383 + 20 Combine like terms: -20 + 20 = 0 0 + x = -146.287388383 + 20 x = -146.287388383 + 20 Combine like terms: -146.287388383 + 20 = -126.287388383 x = -126.287388383 Simplifying x = -126.287388383Solution
The solution to the problem is based on the solutions from the subproblems. x = {166.287388383, -126.287388383}
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