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Simplifying (2x + 2)(x + 3) = 60 Reorder the terms: (2 + 2x)(x + 3) = 60 Reorder the terms: (2 + 2x)(3 + x) = 60 Multiply (2 + 2x) * (3 + x) (2(3 + x) + 2x * (3 + x)) = 60 ((3 * 2 + x * 2) + 2x * (3 + x)) = 60 ((6 + 2x) + 2x * (3 + x)) = 60 (6 + 2x + (3 * 2x + x * 2x)) = 60 (6 + 2x + (6x + 2x2)) = 60 Combine like terms: 2x + 6x = 8x (6 + 8x + 2x2) = 60 Solving 6 + 8x + 2x2 = 60 Solving for variable 'x'. Reorder the terms: 6 + -60 + 8x + 2x2 = 60 + -60 Combine like terms: 6 + -60 = -54 -54 + 8x + 2x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -54 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 4x + x2)' equal to zero and attempt to solve: Simplifying -27 + 4x + x2 = 0 Solving -27 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 4x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 4x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4x + x2 = 0 + 27 4x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 4x + x2 = 27 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 = 27 + 4 Reorder the terms: 4 + 4x + x2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + 4x + x2 = 31 Factor a perfect square on the left side: (x + 2)(x + 2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 2) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 2 = 5.567764363 Simplifying x + 2 = 5.567764363 Reorder the terms: 2 + x = 5.567764363 Solving 2 + x = 5.567764363 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 = 5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.567764363 + -2 x = 5.567764363 + -2 Combine like terms: 5.567764363 + -2 = 3.567764363 x = 3.567764363 Simplifying x = 3.567764363Subproblem 2
x + 2 = -5.567764363 Simplifying x + 2 = -5.567764363 Reorder the terms: 2 + x = -5.567764363 Solving 2 + x = -5.567764363 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 = -5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.567764363 + -2 x = -5.567764363 + -2 Combine like terms: -5.567764363 + -2 = -7.567764363 x = -7.567764363 Simplifying x = -7.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.567764363, -7.567764363}Solution
x = {3.567764363, -7.567764363}
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