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Simplifying (x + -2)(x + 7) = 7 Reorder the terms: (-2 + x)(x + 7) = 7 Reorder the terms: (-2 + x)(7 + x) = 7 Multiply (-2 + x) * (7 + x) (-2(7 + x) + x(7 + x)) = 7 ((7 * -2 + x * -2) + x(7 + x)) = 7 ((-14 + -2x) + x(7 + x)) = 7 (-14 + -2x + (7 * x + x * x)) = 7 (-14 + -2x + (7x + x2)) = 7 Combine like terms: -2x + 7x = 5x (-14 + 5x + x2) = 7 Solving -14 + 5x + x2 = 7 Solving for variable 'x'. Reorder the terms: -14 + -7 + 5x + x2 = 7 + -7 Combine like terms: -14 + -7 = -21 -21 + 5x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -21 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5x + x2 = 0 + 21 5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 5x + x2 = 21 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 = 21 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + 5x + x2 = 27.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 2.5 = 5.220153254 Simplifying x + 2.5 = 5.220153254 Reorder the terms: 2.5 + x = 5.220153254 Solving 2.5 + x = 5.220153254 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 = 5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.220153254 + -2.5 x = 5.220153254 + -2.5 Combine like terms: 5.220153254 + -2.5 = 2.720153254 x = 2.720153254 Simplifying x = 2.720153254Subproblem 2
x + 2.5 = -5.220153254 Simplifying x + 2.5 = -5.220153254 Reorder the terms: 2.5 + x = -5.220153254 Solving 2.5 + x = -5.220153254 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 = -5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.220153254 + -2.5 x = -5.220153254 + -2.5 Combine like terms: -5.220153254 + -2.5 = -7.720153254 x = -7.720153254 Simplifying x = -7.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.720153254, -7.720153254}
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