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Simplifying 14x2 + 15x + -5 = 0 Reorder the terms: -5 + 15x + 14x2 = 0 Solving -5 + 15x + 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'. -0.3571428571 + 1.071428571x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + 1.071428571x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + 1.071428571x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + 1.071428571x + x2 = 0 + 0.3571428571 1.071428571x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 1.071428571x + x2 = 0.3571428571 The x term is 1.071428571x. Take half its coefficient (0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. 1.071428571x + 0.2869897957 + x2 = 0.3571428571 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571x + x2 = 0.3571428571 + 0.2869897957 Combine like terms: 0.3571428571 + 0.2869897957 = 0.6441326528 0.2869897957 + 1.071428571x + x2 = 0.6441326528 Factor a perfect square on the left side: (x + 0.5357142855)(x + 0.5357142855) = 0.6441326528 Calculate the square root of the right side: 0.802578752 Break this problem into two subproblems by setting (x + 0.5357142855) equal to 0.802578752 and -0.802578752.Subproblem 1
x + 0.5357142855 = 0.802578752 Simplifying x + 0.5357142855 = 0.802578752 Reorder the terms: 0.5357142855 + x = 0.802578752 Solving 0.5357142855 + x = 0.802578752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = 0.802578752 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = 0.802578752 + -0.5357142855 x = 0.802578752 + -0.5357142855 Combine like terms: 0.802578752 + -0.5357142855 = 0.2668644665 x = 0.2668644665 Simplifying x = 0.2668644665Subproblem 2
x + 0.5357142855 = -0.802578752 Simplifying x + 0.5357142855 = -0.802578752 Reorder the terms: 0.5357142855 + x = -0.802578752 Solving 0.5357142855 + x = -0.802578752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = -0.802578752 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = -0.802578752 + -0.5357142855 x = -0.802578752 + -0.5357142855 Combine like terms: -0.802578752 + -0.5357142855 = -1.3382930375 x = -1.3382930375 Simplifying x = -1.3382930375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2668644665, -1.3382930375}
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