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Simplifying 3(4x + -1)(4x + 3) = 49x Reorder the terms: 3(-1 + 4x)(4x + 3) = 49x Reorder the terms: 3(-1 + 4x)(3 + 4x) = 49x Multiply (-1 + 4x) * (3 + 4x) 3(-1(3 + 4x) + 4x * (3 + 4x)) = 49x 3((3 * -1 + 4x * -1) + 4x * (3 + 4x)) = 49x 3((-3 + -4x) + 4x * (3 + 4x)) = 49x 3(-3 + -4x + (3 * 4x + 4x * 4x)) = 49x 3(-3 + -4x + (12x + 16x2)) = 49x Combine like terms: -4x + 12x = 8x 3(-3 + 8x + 16x2) = 49x (-3 * 3 + 8x * 3 + 16x2 * 3) = 49x (-9 + 24x + 48x2) = 49x Solving -9 + 24x + 48x2 = 49x Solving for variable 'x'. Reorder the terms: -9 + 24x + -49x + 48x2 = 49x + -49x Combine like terms: 24x + -49x = -25x -9 + -25x + 48x2 = 49x + -49x Combine like terms: 49x + -49x = 0 -9 + -25x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.1875 + -0.5208333333x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.5208333333x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.5208333333x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.5208333333x + x2 = 0 + 0.1875 -0.5208333333x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.5208333333x + x2 = 0.1875 The x term is -0.5208333333x. Take half its coefficient (-0.2604166667). Square it (0.06781684030) and add it to both sides. Add '0.06781684030' to each side of the equation. -0.5208333333x + 0.06781684030 + x2 = 0.1875 + 0.06781684030 Reorder the terms: 0.06781684030 + -0.5208333333x + x2 = 0.1875 + 0.06781684030 Combine like terms: 0.1875 + 0.06781684030 = 0.2553168403 0.06781684030 + -0.5208333333x + x2 = 0.2553168403 Factor a perfect square on the left side: (x + -0.2604166667)(x + -0.2604166667) = 0.2553168403 Calculate the square root of the right side: 0.505288868 Break this problem into two subproblems by setting (x + -0.2604166667) equal to 0.505288868 and -0.505288868.Subproblem 1
x + -0.2604166667 = 0.505288868 Simplifying x + -0.2604166667 = 0.505288868 Reorder the terms: -0.2604166667 + x = 0.505288868 Solving -0.2604166667 + x = 0.505288868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2604166667' to each side of the equation. -0.2604166667 + 0.2604166667 + x = 0.505288868 + 0.2604166667 Combine like terms: -0.2604166667 + 0.2604166667 = 0.0000000000 0.0000000000 + x = 0.505288868 + 0.2604166667 x = 0.505288868 + 0.2604166667 Combine like terms: 0.505288868 + 0.2604166667 = 0.7657055347 x = 0.7657055347 Simplifying x = 0.7657055347Subproblem 2
x + -0.2604166667 = -0.505288868 Simplifying x + -0.2604166667 = -0.505288868 Reorder the terms: -0.2604166667 + x = -0.505288868 Solving -0.2604166667 + x = -0.505288868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2604166667' to each side of the equation. -0.2604166667 + 0.2604166667 + x = -0.505288868 + 0.2604166667 Combine like terms: -0.2604166667 + 0.2604166667 = 0.0000000000 0.0000000000 + x = -0.505288868 + 0.2604166667 x = -0.505288868 + 0.2604166667 Combine like terms: -0.505288868 + 0.2604166667 = -0.2448722013 x = -0.2448722013 Simplifying x = -0.2448722013Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7657055347, -0.2448722013}
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