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Simplifying 20x2 + -174x + 35 = 0 Reorder the terms: 35 + -174x + 20x2 = 0 Solving 35 + -174x + 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'. 1.75 + -8.7x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -8.7x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -8.7x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -8.7x + x2 = 0 + -1.75 -8.7x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -8.7x + x2 = -1.75 The x term is -8.7x. Take half its coefficient (-4.35). Square it (18.9225) and add it to both sides. Add '18.9225' to each side of the equation. -8.7x + 18.9225 + x2 = -1.75 + 18.9225 Reorder the terms: 18.9225 + -8.7x + x2 = -1.75 + 18.9225 Combine like terms: -1.75 + 18.9225 = 17.1725 18.9225 + -8.7x + x2 = 17.1725 Factor a perfect square on the left side: (x + -4.35)(x + -4.35) = 17.1725 Calculate the square root of the right side: 4.143971525 Break this problem into two subproblems by setting (x + -4.35) equal to 4.143971525 and -4.143971525.Subproblem 1
x + -4.35 = 4.143971525 Simplifying x + -4.35 = 4.143971525 Reorder the terms: -4.35 + x = 4.143971525 Solving -4.35 + x = 4.143971525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.35' to each side of the equation. -4.35 + 4.35 + x = 4.143971525 + 4.35 Combine like terms: -4.35 + 4.35 = 0.00 0.00 + x = 4.143971525 + 4.35 x = 4.143971525 + 4.35 Combine like terms: 4.143971525 + 4.35 = 8.493971525 x = 8.493971525 Simplifying x = 8.493971525Subproblem 2
x + -4.35 = -4.143971525 Simplifying x + -4.35 = -4.143971525 Reorder the terms: -4.35 + x = -4.143971525 Solving -4.35 + x = -4.143971525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.35' to each side of the equation. -4.35 + 4.35 + x = -4.143971525 + 4.35 Combine like terms: -4.35 + 4.35 = 0.00 0.00 + x = -4.143971525 + 4.35 x = -4.143971525 + 4.35 Combine like terms: -4.143971525 + 4.35 = 0.206028475 x = 0.206028475 Simplifying x = 0.206028475Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.493971525, 0.206028475}
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