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Simplifying (2x + -7)(x + -11) = 3 Reorder the terms: (-7 + 2x)(x + -11) = 3 Reorder the terms: (-7 + 2x)(-11 + x) = 3 Multiply (-7 + 2x) * (-11 + x) (-7(-11 + x) + 2x * (-11 + x)) = 3 ((-11 * -7 + x * -7) + 2x * (-11 + x)) = 3 ((77 + -7x) + 2x * (-11 + x)) = 3 (77 + -7x + (-11 * 2x + x * 2x)) = 3 (77 + -7x + (-22x + 2x2)) = 3 Combine like terms: -7x + -22x = -29x (77 + -29x + 2x2) = 3 Solving 77 + -29x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: 77 + -3 + -29x + 2x2 = 3 + -3 Combine like terms: 77 + -3 = 74 74 + -29x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 74 + -29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 37 + -14.5x + x2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -14.5x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + -14.5x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -14.5x + x2 = 0 + -37 -14.5x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 -14.5x + x2 = -37 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = -37 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -37 + 52.5625 Combine like terms: -37 + 52.5625 = 15.5625 52.5625 + -14.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -7.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -7.25 = 3.94493346 Simplifying x + -7.25 = 3.94493346 Reorder the terms: -7.25 + x = 3.94493346 Solving -7.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 3.94493346 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 3.94493346 + 7.25 x = 3.94493346 + 7.25 Combine like terms: 3.94493346 + 7.25 = 11.19493346 x = 11.19493346 Simplifying x = 11.19493346Subproblem 2
x + -7.25 = -3.94493346 Simplifying x + -7.25 = -3.94493346 Reorder the terms: -7.25 + x = -3.94493346 Solving -7.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -3.94493346 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -3.94493346 + 7.25 x = -3.94493346 + 7.25 Combine like terms: -3.94493346 + 7.25 = 3.30506654 x = 3.30506654 Simplifying x = 3.30506654Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.19493346, 3.30506654}
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