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Simplifying 8(x + 3) * 23(x + -7) = 55 Reorder the terms: 8(3 + x) * 23(x + -7) = 55 Reorder the terms: 8(3 + x) * 23(-7 + x) = 55 Reorder the terms for easier multiplication: 8 * 23(3 + x)(-7 + x) = 55 Multiply 8 * 23 184(3 + x)(-7 + x) = 55 Multiply (3 + x) * (-7 + x) 184(3(-7 + x) + x(-7 + x)) = 55 184((-7 * 3 + x * 3) + x(-7 + x)) = 55 184((-21 + 3x) + x(-7 + x)) = 55 184(-21 + 3x + (-7 * x + x * x)) = 55 184(-21 + 3x + (-7x + x2)) = 55 Combine like terms: 3x + -7x = -4x 184(-21 + -4x + x2) = 55 (-21 * 184 + -4x * 184 + x2 * 184) = 55 (-3864 + -736x + 184x2) = 55 Solving -3864 + -736x + 184x2 = 55 Solving for variable 'x'. Reorder the terms: -3864 + -55 + -736x + 184x2 = 55 + -55 Combine like terms: -3864 + -55 = -3919 -3919 + -736x + 184x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -3919 + -736x + 184x2 = 0 Begin completing the square. Divide all terms by 184 the coefficient of the squared term: Divide each side by '184'. -21.29891304 + -4x + x2 = 0 Move the constant term to the right: Add '21.29891304' to each side of the equation. -21.29891304 + -4x + 21.29891304 + x2 = 0 + 21.29891304 Reorder the terms: -21.29891304 + 21.29891304 + -4x + x2 = 0 + 21.29891304 Combine like terms: -21.29891304 + 21.29891304 = 0.00000000 0.00000000 + -4x + x2 = 0 + 21.29891304 -4x + x2 = 0 + 21.29891304 Combine like terms: 0 + 21.29891304 = 21.29891304 -4x + x2 = 21.29891304 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 21.29891304 + 4 Reorder the terms: 4 + -4x + x2 = 21.29891304 + 4 Combine like terms: 21.29891304 + 4 = 25.29891304 4 + -4x + x2 = 25.29891304 Factor a perfect square on the left side: (x + -2)(x + -2) = 25.29891304 Calculate the square root of the right side: 5.029802485 Break this problem into two subproblems by setting (x + -2) equal to 5.029802485 and -5.029802485.Subproblem 1
x + -2 = 5.029802485 Simplifying x + -2 = 5.029802485 Reorder the terms: -2 + x = 5.029802485 Solving -2 + x = 5.029802485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.029802485 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.029802485 + 2 x = 5.029802485 + 2 Combine like terms: 5.029802485 + 2 = 7.029802485 x = 7.029802485 Simplifying x = 7.029802485Subproblem 2
x + -2 = -5.029802485 Simplifying x + -2 = -5.029802485 Reorder the terms: -2 + x = -5.029802485 Solving -2 + x = -5.029802485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.029802485 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.029802485 + 2 x = -5.029802485 + 2 Combine like terms: -5.029802485 + 2 = -3.029802485 x = -3.029802485 Simplifying x = -3.029802485Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.029802485, -3.029802485}
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