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Simplifying 2x2 + 17 = 20x Reorder the terms: 17 + 2x2 = 20x Solving 17 + 2x2 = 20x Solving for variable 'x'. Reorder the terms: 17 + -20x + 2x2 = 20x + -20x Combine like terms: 20x + -20x = 0 17 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -10x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -10x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -10x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -10x + x2 = 0 + -8.5 -10x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -10x + x2 = -8.5 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 = -8.5 + 25 Reorder the terms: 25 + -10x + x2 = -8.5 + 25 Combine like terms: -8.5 + 25 = 16.5 25 + -10x + x2 = 16.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x + -5) equal to 4.062019202 and -4.062019202.Subproblem 1
x + -5 = 4.062019202 Simplifying x + -5 = 4.062019202 Reorder the terms: -5 + x = 4.062019202 Solving -5 + x = 4.062019202 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 = 4.062019202 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.062019202 + 5 x = 4.062019202 + 5 Combine like terms: 4.062019202 + 5 = 9.062019202 x = 9.062019202 Simplifying x = 9.062019202Subproblem 2
x + -5 = -4.062019202 Simplifying x + -5 = -4.062019202 Reorder the terms: -5 + x = -4.062019202 Solving -5 + x = -4.062019202 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 = -4.062019202 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.062019202 + 5 x = -4.062019202 + 5 Combine like terms: -4.062019202 + 5 = 0.937980798 x = 0.937980798 Simplifying x = 0.937980798Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.062019202, 0.937980798}
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