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Simplifying 19x2 + -646x + 5475 = 0 Reorder the terms: 5475 + -646x + 19x2 = 0 Solving 5475 + -646x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 288.1578947 + -34x + x2 = 0 Move the constant term to the right: Add '-288.1578947' to each side of the equation. 288.1578947 + -34x + -288.1578947 + x2 = 0 + -288.1578947 Reorder the terms: 288.1578947 + -288.1578947 + -34x + x2 = 0 + -288.1578947 Combine like terms: 288.1578947 + -288.1578947 = 0.0000000 0.0000000 + -34x + x2 = 0 + -288.1578947 -34x + x2 = 0 + -288.1578947 Combine like terms: 0 + -288.1578947 = -288.1578947 -34x + x2 = -288.1578947 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -288.1578947 + 289 Reorder the terms: 289 + -34x + x2 = -288.1578947 + 289 Combine like terms: -288.1578947 + 289 = 0.8421053 289 + -34x + x2 = 0.8421053 Factor a perfect square on the left side: (x + -17)(x + -17) = 0.8421053 Calculate the square root of the right side: 0.917662956 Break this problem into two subproblems by setting (x + -17) equal to 0.917662956 and -0.917662956.Subproblem 1
x + -17 = 0.917662956 Simplifying x + -17 = 0.917662956 Reorder the terms: -17 + x = 0.917662956 Solving -17 + x = 0.917662956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0.917662956 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0.917662956 + 17 x = 0.917662956 + 17 Combine like terms: 0.917662956 + 17 = 17.917662956 x = 17.917662956 Simplifying x = 17.917662956Subproblem 2
x + -17 = -0.917662956 Simplifying x + -17 = -0.917662956 Reorder the terms: -17 + x = -0.917662956 Solving -17 + x = -0.917662956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -0.917662956 + 17 Combine like terms: -17 + 17 = 0 0 + x = -0.917662956 + 17 x = -0.917662956 + 17 Combine like terms: -0.917662956 + 17 = 16.082337044 x = 16.082337044 Simplifying x = 16.082337044Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.917662956, 16.082337044}
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