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Simplifying 0 = x2 + (-20) * x + 40 Reorder the terms: 0 = 40 + -20x + x2 Solving 0 = 40 + -20x + x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + 20x + -1x2 = 40 + -20x + x2 + -40 + 20x + -1x2 Reorder the terms: -40 + 20x + -1x2 = 40 + -40 + -20x + 20x + x2 + -1x2 Combine like terms: 40 + -40 = 0 -40 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 -40 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 -40 + 20x + -1x2 = 0 + x2 + -1x2 -40 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -40 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -20x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -20x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -20x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -20x + x2 = 0 + -40 -20x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -20x + x2 = -40 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -40 + 100 Reorder the terms: 100 + -20x + x2 = -40 + 100 Combine like terms: -40 + 100 = 60 100 + -20x + x2 = 60 Factor a perfect square on the left side: (x + -10)(x + -10) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -10) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -10 = 7.745966692 Simplifying x + -10 = 7.745966692 Reorder the terms: -10 + x = 7.745966692 Solving -10 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.745966692 + 10 x = 7.745966692 + 10 Combine like terms: 7.745966692 + 10 = 17.745966692 x = 17.745966692 Simplifying x = 17.745966692Subproblem 2
x + -10 = -7.745966692 Simplifying x + -10 = -7.745966692 Reorder the terms: -10 + x = -7.745966692 Solving -10 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.745966692 + 10 x = -7.745966692 + 10 Combine like terms: -7.745966692 + 10 = 2.254033308 x = 2.254033308 Simplifying x = 2.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.745966692, 2.254033308}
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