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Simplifying 2x + -4x(3 + 7x) = 3 + -8 2x + (3 * -4x + 7x * -4x) = 3 + -8 2x + (-12x + -28x2) = 3 + -8 Combine like terms: 2x + -12x = -10x -10x + -28x2 = 3 + -8 Combine like terms: 3 + -8 = -5 -10x + -28x2 = -5 Solving -10x + -28x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + -10x + -28x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -10x + -28x2 = 0 Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. -0.1785714286 + 0.3571428571x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.3571428571x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + 0.3571428571x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + 0.3571428571x + x2 = 0 + 0.1785714286 0.3571428571x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 0.3571428571x + x2 = 0.1785714286 The x term is 0.3571428571x. Take half its coefficient (0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. 0.3571428571x + 0.03188775511 + x2 = 0.1785714286 + 0.03188775511 Reorder the terms: 0.03188775511 + 0.3571428571x + x2 = 0.1785714286 + 0.03188775511 Combine like terms: 0.1785714286 + 0.03188775511 = 0.21045918371 0.03188775511 + 0.3571428571x + x2 = 0.21045918371 Factor a perfect square on the left side: (x + 0.1785714286)(x + 0.1785714286) = 0.21045918371 Calculate the square root of the right side: 0.458758306 Break this problem into two subproblems by setting (x + 0.1785714286) equal to 0.458758306 and -0.458758306.Subproblem 1
x + 0.1785714286 = 0.458758306 Simplifying x + 0.1785714286 = 0.458758306 Reorder the terms: 0.1785714286 + x = 0.458758306 Solving 0.1785714286 + x = 0.458758306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + x = 0.458758306 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + x = 0.458758306 + -0.1785714286 x = 0.458758306 + -0.1785714286 Combine like terms: 0.458758306 + -0.1785714286 = 0.2801868774 x = 0.2801868774 Simplifying x = 0.2801868774Subproblem 2
x + 0.1785714286 = -0.458758306 Simplifying x + 0.1785714286 = -0.458758306 Reorder the terms: 0.1785714286 + x = -0.458758306 Solving 0.1785714286 + x = -0.458758306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + x = -0.458758306 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + x = -0.458758306 + -0.1785714286 x = -0.458758306 + -0.1785714286 Combine like terms: -0.458758306 + -0.1785714286 = -0.6373297346 x = -0.6373297346 Simplifying x = -0.6373297346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2801868774, -0.6373297346}
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