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Simplifying 40x + -1x2 + 1 = 0 Reorder the terms: 1 + 40x + -1x2 = 0 Solving 1 + 40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -40x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -40x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -40x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -40x + x2 = 0 + 1 -40x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -40x + x2 = 1 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 = 1 + 400 Reorder the terms: 400 + -40x + x2 = 1 + 400 Combine like terms: 1 + 400 = 401 400 + -40x + x2 = 401 Factor a perfect square on the left side: (x + -20)(x + -20) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + -20) equal to 20.024984395 and -20.024984395.Subproblem 1
x + -20 = 20.024984395 Simplifying x + -20 = 20.024984395 Reorder the terms: -20 + x = 20.024984395 Solving -20 + x = 20.024984395 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 = 20.024984395 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.024984395 + 20 x = 20.024984395 + 20 Combine like terms: 20.024984395 + 20 = 40.024984395 x = 40.024984395 Simplifying x = 40.024984395Subproblem 2
x + -20 = -20.024984395 Simplifying x + -20 = -20.024984395 Reorder the terms: -20 + x = -20.024984395 Solving -20 + x = -20.024984395 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 = -20.024984395 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.024984395 + 20 x = -20.024984395 + 20 Combine like terms: -20.024984395 + 20 = -0.024984395 x = -0.024984395 Simplifying x = -0.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.024984395, -0.024984395}
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