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Simplifying (2(x + 3))(x + -1) = 66 Reorder the terms: (2(3 + x))(x + -1) = 66 ((3 * 2 + x * 2))(x + -1) = 66 ((6 + 2x))(x + -1) = 66 Reorder the terms: (6 + 2x)(-1 + x) = 66 Multiply (6 + 2x) * (-1 + x) (6(-1 + x) + 2x * (-1 + x)) = 66 ((-1 * 6 + x * 6) + 2x * (-1 + x)) = 66 ((-6 + 6x) + 2x * (-1 + x)) = 66 (-6 + 6x + (-1 * 2x + x * 2x)) = 66 (-6 + 6x + (-2x + 2x2)) = 66 Combine like terms: 6x + -2x = 4x (-6 + 4x + 2x2) = 66 Solving -6 + 4x + 2x2 = 66 Solving for variable 'x'. Reorder the terms: -6 + -66 + 4x + 2x2 = 66 + -66 Combine like terms: -6 + -66 = -72 -72 + 4x + 2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -72 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 2x + x2)' equal to zero and attempt to solve: Simplifying -36 + 2x + x2 = 0 Solving -36 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 2x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 2x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 2x + x2 = 0 + 36 2x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 2x + x2 = 36 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 36 + 1 Reorder the terms: 1 + 2x + x2 = 36 + 1 Combine like terms: 36 + 1 = 37 1 + 2x + x2 = 37 Factor a perfect square on the left side: (x + 1)(x + 1) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 1) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 1 = 6.08276253 Simplifying x + 1 = 6.08276253 Reorder the terms: 1 + x = 6.08276253 Solving 1 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.08276253 + -1 x = 6.08276253 + -1 Combine like terms: 6.08276253 + -1 = 5.08276253 x = 5.08276253 Simplifying x = 5.08276253Subproblem 2
x + 1 = -6.08276253 Simplifying x + 1 = -6.08276253 Reorder the terms: 1 + x = -6.08276253 Solving 1 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.08276253 + -1 x = -6.08276253 + -1 Combine like terms: -6.08276253 + -1 = -7.08276253 x = -7.08276253 Simplifying x = -7.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.08276253, -7.08276253}Solution
x = {5.08276253, -7.08276253}
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