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Simplifying 14x2 + -29x + 0.84 = 0 Reorder the terms: 0.84 + -29x + 14x2 = 0 Solving 0.84 + -29x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.06 + -2.071428571x + x2 = 0 Move the constant term to the right: Add '-0.06' to each side of the equation. 0.06 + -2.071428571x + -0.06 + x2 = 0 + -0.06 Reorder the terms: 0.06 + -0.06 + -2.071428571x + x2 = 0 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + -2.071428571x + x2 = 0 + -0.06 -2.071428571x + x2 = 0 + -0.06 Combine like terms: 0 + -0.06 = -0.06 -2.071428571x + x2 = -0.06 The x term is -2.071428571x. Take half its coefficient (-1.035714286). Square it (1.072704082) and add it to both sides. Add '1.072704082' to each side of the equation. -2.071428571x + 1.072704082 + x2 = -0.06 + 1.072704082 Reorder the terms: 1.072704082 + -2.071428571x + x2 = -0.06 + 1.072704082 Combine like terms: -0.06 + 1.072704082 = 1.012704082 1.072704082 + -2.071428571x + x2 = 1.012704082 Factor a perfect square on the left side: (x + -1.035714286)(x + -1.035714286) = 1.012704082 Calculate the square root of the right side: 1.006331994 Break this problem into two subproblems by setting (x + -1.035714286) equal to 1.006331994 and -1.006331994.Subproblem 1
x + -1.035714286 = 1.006331994 Simplifying x + -1.035714286 = 1.006331994 Reorder the terms: -1.035714286 + x = 1.006331994 Solving -1.035714286 + x = 1.006331994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.035714286' to each side of the equation. -1.035714286 + 1.035714286 + x = 1.006331994 + 1.035714286 Combine like terms: -1.035714286 + 1.035714286 = 0.000000000 0.000000000 + x = 1.006331994 + 1.035714286 x = 1.006331994 + 1.035714286 Combine like terms: 1.006331994 + 1.035714286 = 2.04204628 x = 2.04204628 Simplifying x = 2.04204628Subproblem 2
x + -1.035714286 = -1.006331994 Simplifying x + -1.035714286 = -1.006331994 Reorder the terms: -1.035714286 + x = -1.006331994 Solving -1.035714286 + x = -1.006331994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.035714286' to each side of the equation. -1.035714286 + 1.035714286 + x = -1.006331994 + 1.035714286 Combine like terms: -1.035714286 + 1.035714286 = 0.000000000 0.000000000 + x = -1.006331994 + 1.035714286 x = -1.006331994 + 1.035714286 Combine like terms: -1.006331994 + 1.035714286 = 0.029382292 x = 0.029382292 Simplifying x = 0.029382292Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.04204628, 0.029382292}
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