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Simplifying x = 40x2 + -400x + 500 Reorder the terms: x = 500 + -400x + 40x2 Solving x = 500 + -400x + 40x2 Solving for variable 'x'. Reorder the terms: -500 + x + 400x + -40x2 = 500 + -400x + 40x2 + -500 + 400x + -40x2 Combine like terms: x + 400x = 401x -500 + 401x + -40x2 = 500 + -400x + 40x2 + -500 + 400x + -40x2 Reorder the terms: -500 + 401x + -40x2 = 500 + -500 + -400x + 400x + 40x2 + -40x2 Combine like terms: 500 + -500 = 0 -500 + 401x + -40x2 = 0 + -400x + 400x + 40x2 + -40x2 -500 + 401x + -40x2 = -400x + 400x + 40x2 + -40x2 Combine like terms: -400x + 400x = 0 -500 + 401x + -40x2 = 0 + 40x2 + -40x2 -500 + 401x + -40x2 = 40x2 + -40x2 Combine like terms: 40x2 + -40x2 = 0 -500 + 401x + -40x2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. 12.5 + -10.025x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -10.025x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -10.025x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -10.025x + x2 = 0 + -12.5 -10.025x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -10.025x + x2 = -12.5 The x term is -10.025x. Take half its coefficient (-5.0125). Square it (25.12515625) and add it to both sides. Add '25.12515625' to each side of the equation. -10.025x + 25.12515625 + x2 = -12.5 + 25.12515625 Reorder the terms: 25.12515625 + -10.025x + x2 = -12.5 + 25.12515625 Combine like terms: -12.5 + 25.12515625 = 12.62515625 25.12515625 + -10.025x + x2 = 12.62515625 Factor a perfect square on the left side: (x + -5.0125)(x + -5.0125) = 12.62515625 Calculate the square root of the right side: 3.553189588 Break this problem into two subproblems by setting (x + -5.0125) equal to 3.553189588 and -3.553189588.Subproblem 1
x + -5.0125 = 3.553189588 Simplifying x + -5.0125 = 3.553189588 Reorder the terms: -5.0125 + x = 3.553189588 Solving -5.0125 + x = 3.553189588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.0125' to each side of the equation. -5.0125 + 5.0125 + x = 3.553189588 + 5.0125 Combine like terms: -5.0125 + 5.0125 = 0.0000 0.0000 + x = 3.553189588 + 5.0125 x = 3.553189588 + 5.0125 Combine like terms: 3.553189588 + 5.0125 = 8.565689588 x = 8.565689588 Simplifying x = 8.565689588Subproblem 2
x + -5.0125 = -3.553189588 Simplifying x + -5.0125 = -3.553189588 Reorder the terms: -5.0125 + x = -3.553189588 Solving -5.0125 + x = -3.553189588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.0125' to each side of the equation. -5.0125 + 5.0125 + x = -3.553189588 + 5.0125 Combine like terms: -5.0125 + 5.0125 = 0.0000 0.0000 + x = -3.553189588 + 5.0125 x = -3.553189588 + 5.0125 Combine like terms: -3.553189588 + 5.0125 = 1.459310412 x = 1.459310412 Simplifying x = 1.459310412Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.565689588, 1.459310412}
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