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Simplifying 7x(4x + -3) = 3(x + 1) Reorder the terms: 7x(-3 + 4x) = 3(x + 1) (-3 * 7x + 4x * 7x) = 3(x + 1) (-21x + 28x2) = 3(x + 1) Reorder the terms: -21x + 28x2 = 3(1 + x) -21x + 28x2 = (1 * 3 + x * 3) -21x + 28x2 = (3 + 3x) Solving -21x + 28x2 = 3 + 3x Solving for variable 'x'. Reorder the terms: -3 + -21x + -3x + 28x2 = 3 + 3x + -3 + -3x Combine like terms: -21x + -3x = -24x -3 + -24x + 28x2 = 3 + 3x + -3 + -3x Reorder the terms: -3 + -24x + 28x2 = 3 + -3 + 3x + -3x Combine like terms: 3 + -3 = 0 -3 + -24x + 28x2 = 0 + 3x + -3x -3 + -24x + 28x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -3 + -24x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1071428571 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + -0.8571428571x + 0.1071428571 + x2 = 0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + -0.8571428571x + x2 = 0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.1071428571 -0.8571428571x + x2 = 0 + 0.1071428571 Combine like terms: 0 + 0.1071428571 = 0.1071428571 -0.8571428571x + x2 = 0.1071428571 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.1071428571 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.1071428571 + 0.1836734694 Combine like terms: 0.1071428571 + 0.1836734694 = 0.2908163265 0.1836734694 + -0.8571428571x + x2 = 0.2908163265 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.2908163265 Calculate the square root of the right side: 0.539273888 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.539273888 and -0.539273888.Subproblem 1
x + -0.4285714286 = 0.539273888 Simplifying x + -0.4285714286 = 0.539273888 Reorder the terms: -0.4285714286 + x = 0.539273888 Solving -0.4285714286 + x = 0.539273888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.539273888 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.539273888 + 0.4285714286 x = 0.539273888 + 0.4285714286 Combine like terms: 0.539273888 + 0.4285714286 = 0.9678453166 x = 0.9678453166 Simplifying x = 0.9678453166Subproblem 2
x + -0.4285714286 = -0.539273888 Simplifying x + -0.4285714286 = -0.539273888 Reorder the terms: -0.4285714286 + x = -0.539273888 Solving -0.4285714286 + x = -0.539273888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.539273888 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.539273888 + 0.4285714286 x = -0.539273888 + 0.4285714286 Combine like terms: -0.539273888 + 0.4285714286 = -0.1107024594 x = -0.1107024594 Simplifying x = -0.1107024594Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9678453166, -0.1107024594}
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