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Simplifying 20x2 + -34x + 11 = 0 Reorder the terms: 11 + -34x + 20x2 = 0 Solving 11 + -34x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.55 + -1.7x + x2 = 0 Move the constant term to the right: Add '-0.55' to each side of the equation. 0.55 + -1.7x + -0.55 + x2 = 0 + -0.55 Reorder the terms: 0.55 + -0.55 + -1.7x + x2 = 0 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + -1.7x + x2 = 0 + -0.55 -1.7x + x2 = 0 + -0.55 Combine like terms: 0 + -0.55 = -0.55 -1.7x + x2 = -0.55 The x term is -1.7x. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7x + 0.7225 + x2 = -0.55 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = -0.55 + 0.7225 Combine like terms: -0.55 + 0.7225 = 0.1725 0.7225 + -1.7x + x2 = 0.1725 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 0.1725 Calculate the square root of the right side: 0.415331193 Break this problem into two subproblems by setting (x + -0.85) equal to 0.415331193 and -0.415331193.Subproblem 1
x + -0.85 = 0.415331193 Simplifying x + -0.85 = 0.415331193 Reorder the terms: -0.85 + x = 0.415331193 Solving -0.85 + x = 0.415331193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = 0.415331193 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 0.415331193 + 0.85 x = 0.415331193 + 0.85 Combine like terms: 0.415331193 + 0.85 = 1.265331193 x = 1.265331193 Simplifying x = 1.265331193Subproblem 2
x + -0.85 = -0.415331193 Simplifying x + -0.85 = -0.415331193 Reorder the terms: -0.85 + x = -0.415331193 Solving -0.85 + x = -0.415331193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = -0.415331193 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -0.415331193 + 0.85 x = -0.415331193 + 0.85 Combine like terms: -0.415331193 + 0.85 = 0.434668807 x = 0.434668807 Simplifying x = 0.434668807Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.265331193, 0.434668807}
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