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Simplifying 2x2 + -20x + 20 = 35 Reorder the terms: 20 + -20x + 2x2 = 35 Solving 20 + -20x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: 20 + -35 + -20x + 2x2 = 35 + -35 Combine like terms: 20 + -35 = -15 -15 + -20x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -15 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -10x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -10x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -10x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -10x + x2 = 0 + 7.5 -10x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -10x + x2 = 7.5 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 = 7.5 + 25 Reorder the terms: 25 + -10x + x2 = 7.5 + 25 Combine like terms: 7.5 + 25 = 32.5 25 + -10x + x2 = 32.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (x + -5) equal to 5.700877125 and -5.700877125.Subproblem 1
x + -5 = 5.700877125 Simplifying x + -5 = 5.700877125 Reorder the terms: -5 + x = 5.700877125 Solving -5 + x = 5.700877125 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 = 5.700877125 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.700877125 + 5 x = 5.700877125 + 5 Combine like terms: 5.700877125 + 5 = 10.700877125 x = 10.700877125 Simplifying x = 10.700877125Subproblem 2
x + -5 = -5.700877125 Simplifying x + -5 = -5.700877125 Reorder the terms: -5 + x = -5.700877125 Solving -5 + x = -5.700877125 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 = -5.700877125 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.700877125 + 5 x = -5.700877125 + 5 Combine like terms: -5.700877125 + 5 = -0.700877125 x = -0.700877125 Simplifying x = -0.700877125Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.700877125, -0.700877125}
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