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Simplifying 14x2 + -22x = 17 Reorder the terms: -22x + 14x2 = 17 Solving -22x + 14x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -22x + 14x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -22x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.214285714 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '1.214285714' to each side of the equation. -1.214285714 + -1.571428571x + 1.214285714 + x2 = 0 + 1.214285714 Reorder the terms: -1.214285714 + 1.214285714 + -1.571428571x + x2 = 0 + 1.214285714 Combine like terms: -1.214285714 + 1.214285714 = 0.000000000 0.000000000 + -1.571428571x + x2 = 0 + 1.214285714 -1.571428571x + x2 = 0 + 1.214285714 Combine like terms: 0 + 1.214285714 = 1.214285714 -1.571428571x + x2 = 1.214285714 The x term is -1.571428571x. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571x + 0.6173469384 + x2 = 1.214285714 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = 1.214285714 + 0.6173469384 Combine like terms: 1.214285714 + 0.6173469384 = 1.8316326524 0.6173469384 + -1.571428571x + x2 = 1.8316326524 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 1.8316326524 Calculate the square root of the right side: 1.353378237 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 1.353378237 and -1.353378237.Subproblem 1
x + -0.7857142855 = 1.353378237 Simplifying x + -0.7857142855 = 1.353378237 Reorder the terms: -0.7857142855 + x = 1.353378237 Solving -0.7857142855 + x = 1.353378237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 1.353378237 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 1.353378237 + 0.7857142855 x = 1.353378237 + 0.7857142855 Combine like terms: 1.353378237 + 0.7857142855 = 2.1390925225 x = 2.1390925225 Simplifying x = 2.1390925225Subproblem 2
x + -0.7857142855 = -1.353378237 Simplifying x + -0.7857142855 = -1.353378237 Reorder the terms: -0.7857142855 + x = -1.353378237 Solving -0.7857142855 + x = -1.353378237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -1.353378237 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -1.353378237 + 0.7857142855 x = -1.353378237 + 0.7857142855 Combine like terms: -1.353378237 + 0.7857142855 = -0.5676639515 x = -0.5676639515 Simplifying x = -0.5676639515Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1390925225, -0.5676639515}
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