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Simplifying (x + -7)(x + -2) = 5 Reorder the terms: (-7 + x)(x + -2) = 5 Reorder the terms: (-7 + x)(-2 + x) = 5 Multiply (-7 + x) * (-2 + x) (-7(-2 + x) + x(-2 + x)) = 5 ((-2 * -7 + x * -7) + x(-2 + x)) = 5 ((14 + -7x) + x(-2 + x)) = 5 (14 + -7x + (-2 * x + x * x)) = 5 (14 + -7x + (-2x + x2)) = 5 Combine like terms: -7x + -2x = -9x (14 + -9x + x2) = 5 Solving 14 + -9x + x2 = 5 Solving for variable 'x'. Reorder the terms: 14 + -5 + -9x + x2 = 5 + -5 Combine like terms: 14 + -5 = 9 9 + -9x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 9 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9x + x2 = 0 + -9 -9x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9x + x2 = -9 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 = -9 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + -9x + x2 = 11.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -4.5 = 3.354101966 Simplifying x + -4.5 = 3.354101966 Reorder the terms: -4.5 + x = 3.354101966 Solving -4.5 + x = 3.354101966 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 = 3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.354101966 + 4.5 x = 3.354101966 + 4.5 Combine like terms: 3.354101966 + 4.5 = 7.854101966 x = 7.854101966 Simplifying x = 7.854101966Subproblem 2
x + -4.5 = -3.354101966 Simplifying x + -4.5 = -3.354101966 Reorder the terms: -4.5 + x = -3.354101966 Solving -4.5 + x = -3.354101966 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 = -3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.354101966 + 4.5 x = -3.354101966 + 4.5 Combine like terms: -3.354101966 + 4.5 = 1.145898034 x = 1.145898034 Simplifying x = 1.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.854101966, 1.145898034}
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