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Simplifying 20x2 + 10 = 200x + -1 Reorder the terms: 10 + 20x2 = 200x + -1 Reorder the terms: 10 + 20x2 = -1 + 200x Solving 10 + 20x2 = -1 + 200x Solving for variable 'x'. Reorder the terms: 10 + 1 + -200x + 20x2 = -1 + 200x + 1 + -200x Combine like terms: 10 + 1 = 11 11 + -200x + 20x2 = -1 + 200x + 1 + -200x Reorder the terms: 11 + -200x + 20x2 = -1 + 1 + 200x + -200x Combine like terms: -1 + 1 = 0 11 + -200x + 20x2 = 0 + 200x + -200x 11 + -200x + 20x2 = 200x + -200x Combine like terms: 200x + -200x = 0 11 + -200x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.55 + -10x + x2 = 0 Move the constant term to the right: Add '-0.55' to each side of the equation. 0.55 + -10x + -0.55 + x2 = 0 + -0.55 Reorder the terms: 0.55 + -0.55 + -10x + x2 = 0 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + -10x + x2 = 0 + -0.55 -10x + x2 = 0 + -0.55 Combine like terms: 0 + -0.55 = -0.55 -10x + x2 = -0.55 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 = -0.55 + 25 Reorder the terms: 25 + -10x + x2 = -0.55 + 25 Combine like terms: -0.55 + 25 = 24.45 25 + -10x + x2 = 24.45 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.45 Calculate the square root of the right side: 4.944694126 Break this problem into two subproblems by setting (x + -5) equal to 4.944694126 and -4.944694126.Subproblem 1
x + -5 = 4.944694126 Simplifying x + -5 = 4.944694126 Reorder the terms: -5 + x = 4.944694126 Solving -5 + x = 4.944694126 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 = 4.944694126 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.944694126 + 5 x = 4.944694126 + 5 Combine like terms: 4.944694126 + 5 = 9.944694126 x = 9.944694126 Simplifying x = 9.944694126Subproblem 2
x + -5 = -4.944694126 Simplifying x + -5 = -4.944694126 Reorder the terms: -5 + x = -4.944694126 Solving -5 + x = -4.944694126 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 = -4.944694126 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.944694126 + 5 x = -4.944694126 + 5 Combine like terms: -4.944694126 + 5 = 0.055305874 x = 0.055305874 Simplifying x = 0.055305874Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.944694126, 0.055305874}
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