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Simplifying (x)(x + 7) = 480 Reorder the terms: x(7 + x) = 480 (7 * x + x * x) = 480 (7x + x2) = 480 Solving 7x + x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 7x + x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 7x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 7x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 7x + x2 = 0 + 480 7x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 7x + x2 = 480 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 480 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 480 + 12.25 Combine like terms: 480 + 12.25 = 492.25 12.25 + 7x + x2 = 492.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 492.25 Calculate the square root of the right side: 22.186707732 Break this problem into two subproblems by setting (x + 3.5) equal to 22.186707732 and -22.186707732.Subproblem 1
x + 3.5 = 22.186707732 Simplifying x + 3.5 = 22.186707732 Reorder the terms: 3.5 + x = 22.186707732 Solving 3.5 + x = 22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 22.186707732 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 22.186707732 + -3.5 x = 22.186707732 + -3.5 Combine like terms: 22.186707732 + -3.5 = 18.686707732 x = 18.686707732 Simplifying x = 18.686707732Subproblem 2
x + 3.5 = -22.186707732 Simplifying x + 3.5 = -22.186707732 Reorder the terms: 3.5 + x = -22.186707732 Solving 3.5 + x = -22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -22.186707732 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -22.186707732 + -3.5 x = -22.186707732 + -3.5 Combine like terms: -22.186707732 + -3.5 = -25.686707732 x = -25.686707732 Simplifying x = -25.686707732Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.686707732, -25.686707732}
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