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Simplifying (x + 3)(x + 11) = 57 Reorder the terms: (3 + x)(x + 11) = 57 Reorder the terms: (3 + x)(11 + x) = 57 Multiply (3 + x) * (11 + x) (3(11 + x) + x(11 + x)) = 57 ((11 * 3 + x * 3) + x(11 + x)) = 57 ((33 + 3x) + x(11 + x)) = 57 (33 + 3x + (11 * x + x * x)) = 57 (33 + 3x + (11x + x2)) = 57 Combine like terms: 3x + 11x = 14x (33 + 14x + x2) = 57 Solving 33 + 14x + x2 = 57 Solving for variable 'x'. Reorder the terms: 33 + -57 + 14x + x2 = 57 + -57 Combine like terms: 33 + -57 = -24 -24 + 14x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -24 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 14x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 14x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 14x + x2 = 0 + 24 14x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 14x + x2 = 24 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 24 + 49 Reorder the terms: 49 + 14x + x2 = 24 + 49 Combine like terms: 24 + 49 = 73 49 + 14x + x2 = 73 Factor a perfect square on the left side: (x + 7)(x + 7) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 7) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 7 = 8.544003745 Simplifying x + 7 = 8.544003745 Reorder the terms: 7 + x = 8.544003745 Solving 7 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 8.544003745 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.544003745 + -7 x = 8.544003745 + -7 Combine like terms: 8.544003745 + -7 = 1.544003745 x = 1.544003745 Simplifying x = 1.544003745Subproblem 2
x + 7 = -8.544003745 Simplifying x + 7 = -8.544003745 Reorder the terms: 7 + x = -8.544003745 Solving 7 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -8.544003745 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.544003745 + -7 x = -8.544003745 + -7 Combine like terms: -8.544003745 + -7 = -15.544003745 x = -15.544003745 Simplifying x = -15.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.544003745, -15.544003745}
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