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Simplifying 0 = 2x2 + -20x + 43 Reorder the terms: 0 = 43 + -20x + 2x2 Solving 0 = 43 + -20x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -43 = -43 -43 + 20x + -2x2 = 43 + -20x + 2x2 + -43 + 20x + -2x2 Reorder the terms: -43 + 20x + -2x2 = 43 + -43 + -20x + 20x + 2x2 + -2x2 Combine like terms: 43 + -43 = 0 -43 + 20x + -2x2 = 0 + -20x + 20x + 2x2 + -2x2 -43 + 20x + -2x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 -43 + 20x + -2x2 = 0 + 2x2 + -2x2 -43 + 20x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -43 + 20x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 21.5 + -10x + x2 = 0 Move the constant term to the right: Add '-21.5' to each side of the equation. 21.5 + -10x + -21.5 + x2 = 0 + -21.5 Reorder the terms: 21.5 + -21.5 + -10x + x2 = 0 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + -10x + x2 = 0 + -21.5 -10x + x2 = 0 + -21.5 Combine like terms: 0 + -21.5 = -21.5 -10x + x2 = -21.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -21.5 + 25 Reorder the terms: 25 + -10x + x2 = -21.5 + 25 Combine like terms: -21.5 + 25 = 3.5 25 + -10x + x2 = 3.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -5) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -5 = 1.870828693 Simplifying x + -5 = 1.870828693 Reorder the terms: -5 + x = 1.870828693 Solving -5 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.870828693 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.870828693 + 5 x = 1.870828693 + 5 Combine like terms: 1.870828693 + 5 = 6.870828693 x = 6.870828693 Simplifying x = 6.870828693Subproblem 2
x + -5 = -1.870828693 Simplifying x + -5 = -1.870828693 Reorder the terms: -5 + x = -1.870828693 Solving -5 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.870828693 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.870828693 + 5 x = -1.870828693 + 5 Combine like terms: -1.870828693 + 5 = 3.129171307 x = 3.129171307 Simplifying x = 3.129171307Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.870828693, 3.129171307}
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