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Simplifying (x + 7)(x + -2) = 336 Reorder the terms: (7 + x)(x + -2) = 336 Reorder the terms: (7 + x)(-2 + x) = 336 Multiply (7 + x) * (-2 + x) (7(-2 + x) + x(-2 + x)) = 336 ((-2 * 7 + x * 7) + x(-2 + x)) = 336 ((-14 + 7x) + x(-2 + x)) = 336 (-14 + 7x + (-2 * x + x * x)) = 336 (-14 + 7x + (-2x + x2)) = 336 Combine like terms: 7x + -2x = 5x (-14 + 5x + x2) = 336 Solving -14 + 5x + x2 = 336 Solving for variable 'x'. Reorder the terms: -14 + -336 + 5x + x2 = 336 + -336 Combine like terms: -14 + -336 = -350 -350 + 5x + x2 = 336 + -336 Combine like terms: 336 + -336 = 0 -350 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + 5x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + 5x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + 5x + x2 = 0 + 350 5x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 5x + x2 = 350 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 350 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 350 + 6.25 Combine like terms: 350 + 6.25 = 356.25 6.25 + 5x + x2 = 356.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + 2.5) equal to 18.874586088 and -18.874586088.Subproblem 1
x + 2.5 = 18.874586088 Simplifying x + 2.5 = 18.874586088 Reorder the terms: 2.5 + x = 18.874586088 Solving 2.5 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 18.874586088 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 18.874586088 + -2.5 x = 18.874586088 + -2.5 Combine like terms: 18.874586088 + -2.5 = 16.374586088 x = 16.374586088 Simplifying x = 16.374586088Subproblem 2
x + 2.5 = -18.874586088 Simplifying x + 2.5 = -18.874586088 Reorder the terms: 2.5 + x = -18.874586088 Solving 2.5 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -18.874586088 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -18.874586088 + -2.5 x = -18.874586088 + -2.5 Combine like terms: -18.874586088 + -2.5 = -21.374586088 x = -21.374586088 Simplifying x = -21.374586088Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.374586088, -21.374586088}
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