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Simplifying (x + 2)(x + 7) = 72 Reorder the terms: (2 + x)(x + 7) = 72 Reorder the terms: (2 + x)(7 + x) = 72 Multiply (2 + x) * (7 + x) (2(7 + x) + x(7 + x)) = 72 ((7 * 2 + x * 2) + x(7 + x)) = 72 ((14 + 2x) + x(7 + x)) = 72 (14 + 2x + (7 * x + x * x)) = 72 (14 + 2x + (7x + x2)) = 72 Combine like terms: 2x + 7x = 9x (14 + 9x + x2) = 72 Solving 14 + 9x + x2 = 72 Solving for variable 'x'. Reorder the terms: 14 + -72 + 9x + x2 = 72 + -72 Combine like terms: 14 + -72 = -58 -58 + 9x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -58 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 9x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 9x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 9x + x2 = 0 + 58 9x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 9x + x2 = 58 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 58 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 58 + 20.25 Combine like terms: 58 + 20.25 = 78.25 20.25 + 9x + x2 = 78.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + 4.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + 4.5 = 8.845903006 Simplifying x + 4.5 = 8.845903006 Reorder the terms: 4.5 + x = 8.845903006 Solving 4.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 8.845903006 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.845903006 + -4.5 x = 8.845903006 + -4.5 Combine like terms: 8.845903006 + -4.5 = 4.345903006 x = 4.345903006 Simplifying x = 4.345903006Subproblem 2
x + 4.5 = -8.845903006 Simplifying x + 4.5 = -8.845903006 Reorder the terms: 4.5 + x = -8.845903006 Solving 4.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -8.845903006 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.845903006 + -4.5 x = -8.845903006 + -4.5 Combine like terms: -8.845903006 + -4.5 = -13.345903006 x = -13.345903006 Simplifying x = -13.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.345903006, -13.345903006}
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