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Simplifying 48 + -1x = 4x(7x) Remove parenthesis around (7x) 48 + -1x = 4x * 7x Reorder the terms for easier multiplication: 48 + -1x = 4 * 7x * x Multiply 4 * 7 48 + -1x = 28x * x Multiply x * x 48 + -1x = 28x2 Solving 48 + -1x = 28x2 Solving for variable 'x'. Combine like terms: 28x2 + -28x2 = 0 48 + -1x + -28x2 = 0 Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. -1.714285714 + 0.03571428571x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + 0.03571428571x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + 0.03571428571x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + 0.03571428571x + x2 = 0 + 1.714285714 0.03571428571x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 0.03571428571x + x2 = 1.714285714 The x term is 0.03571428571x. Take half its coefficient (0.01785714286). Square it (0.0003188775511) and add it to both sides. Add '0.0003188775511' to each side of the equation. 0.03571428571x + 0.0003188775511 + x2 = 1.714285714 + 0.0003188775511 Reorder the terms: 0.0003188775511 + 0.03571428571x + x2 = 1.714285714 + 0.0003188775511 Combine like terms: 1.714285714 + 0.0003188775511 = 1.7146045915511 0.0003188775511 + 0.03571428571x + x2 = 1.7146045915511 Factor a perfect square on the left side: (x + 0.01785714286)(x + 0.01785714286) = 1.7146045915511 Calculate the square root of the right side: 1.309429109 Break this problem into two subproblems by setting (x + 0.01785714286) equal to 1.309429109 and -1.309429109.Subproblem 1
x + 0.01785714286 = 1.309429109 Simplifying x + 0.01785714286 = 1.309429109 Reorder the terms: 0.01785714286 + x = 1.309429109 Solving 0.01785714286 + x = 1.309429109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01785714286' to each side of the equation. 0.01785714286 + -0.01785714286 + x = 1.309429109 + -0.01785714286 Combine like terms: 0.01785714286 + -0.01785714286 = 0.00000000000 0.00000000000 + x = 1.309429109 + -0.01785714286 x = 1.309429109 + -0.01785714286 Combine like terms: 1.309429109 + -0.01785714286 = 1.29157196614 x = 1.29157196614 Simplifying x = 1.29157196614Subproblem 2
x + 0.01785714286 = -1.309429109 Simplifying x + 0.01785714286 = -1.309429109 Reorder the terms: 0.01785714286 + x = -1.309429109 Solving 0.01785714286 + x = -1.309429109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01785714286' to each side of the equation. 0.01785714286 + -0.01785714286 + x = -1.309429109 + -0.01785714286 Combine like terms: 0.01785714286 + -0.01785714286 = 0.00000000000 0.00000000000 + x = -1.309429109 + -0.01785714286 x = -1.309429109 + -0.01785714286 Combine like terms: -1.309429109 + -0.01785714286 = -1.32728625186 x = -1.32728625186 Simplifying x = -1.32728625186Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29157196614, -1.32728625186}
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