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Simplifying (x + 3)(x + 7) = 48 Reorder the terms: (3 + x)(x + 7) = 48 Reorder the terms: (3 + x)(7 + x) = 48 Multiply (3 + x) * (7 + x) (3(7 + x) + x(7 + x)) = 48 ((7 * 3 + x * 3) + x(7 + x)) = 48 ((21 + 3x) + x(7 + x)) = 48 (21 + 3x + (7 * x + x * x)) = 48 (21 + 3x + (7x + x2)) = 48 Combine like terms: 3x + 7x = 10x (21 + 10x + x2) = 48 Solving 21 + 10x + x2 = 48 Solving for variable 'x'. Reorder the terms: 21 + -48 + 10x + x2 = 48 + -48 Combine like terms: 21 + -48 = -27 -27 + 10x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -27 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 10x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 10x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 10x + x2 = 0 + 27 10x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 10x + x2 = 27 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 27 + 25 Reorder the terms: 25 + 10x + x2 = 27 + 25 Combine like terms: 27 + 25 = 52 25 + 10x + x2 = 52 Factor a perfect square on the left side: (x + 5)(x + 5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 5) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 5 = 7.211102551 Simplifying x + 5 = 7.211102551 Reorder the terms: 5 + x = 7.211102551 Solving 5 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.211102551 + -5 x = 7.211102551 + -5 Combine like terms: 7.211102551 + -5 = 2.211102551 x = 2.211102551 Simplifying x = 2.211102551Subproblem 2
x + 5 = -7.211102551 Simplifying x + 5 = -7.211102551 Reorder the terms: 5 + x = -7.211102551 Solving 5 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.211102551 + -5 x = -7.211102551 + -5 Combine like terms: -7.211102551 + -5 = -12.211102551 x = -12.211102551 Simplifying x = -12.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.211102551, -12.211102551}
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