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Simplifying x2 + 40x + -810 = 0 Reorder the terms: -810 + 40x + x2 = 0 Solving -810 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '810' to each side of the equation. -810 + 40x + 810 + x2 = 0 + 810 Reorder the terms: -810 + 810 + 40x + x2 = 0 + 810 Combine like terms: -810 + 810 = 0 0 + 40x + x2 = 0 + 810 40x + x2 = 0 + 810 Combine like terms: 0 + 810 = 810 40x + x2 = 810 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 = 810 + 400 Reorder the terms: 400 + 40x + x2 = 810 + 400 Combine like terms: 810 + 400 = 1210 400 + 40x + x2 = 1210 Factor a perfect square on the left side: (x + 20)(x + 20) = 1210 Calculate the square root of the right side: 34.785054262 Break this problem into two subproblems by setting (x + 20) equal to 34.785054262 and -34.785054262.Subproblem 1
x + 20 = 34.785054262 Simplifying x + 20 = 34.785054262 Reorder the terms: 20 + x = 34.785054262 Solving 20 + x = 34.785054262 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 = 34.785054262 + -20 Combine like terms: 20 + -20 = 0 0 + x = 34.785054262 + -20 x = 34.785054262 + -20 Combine like terms: 34.785054262 + -20 = 14.785054262 x = 14.785054262 Simplifying x = 14.785054262Subproblem 2
x + 20 = -34.785054262 Simplifying x + 20 = -34.785054262 Reorder the terms: 20 + x = -34.785054262 Solving 20 + x = -34.785054262 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 = -34.785054262 + -20 Combine like terms: 20 + -20 = 0 0 + x = -34.785054262 + -20 x = -34.785054262 + -20 Combine like terms: -34.785054262 + -20 = -54.785054262 x = -54.785054262 Simplifying x = -54.785054262Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.785054262, -54.785054262}
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