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Simplifying (x + 2)(x + -7) = 18 Reorder the terms: (2 + x)(x + -7) = 18 Reorder the terms: (2 + x)(-7 + x) = 18 Multiply (2 + x) * (-7 + x) (2(-7 + x) + x(-7 + x)) = 18 ((-7 * 2 + x * 2) + x(-7 + x)) = 18 ((-14 + 2x) + x(-7 + x)) = 18 (-14 + 2x + (-7 * x + x * x)) = 18 (-14 + 2x + (-7x + x2)) = 18 Combine like terms: 2x + -7x = -5x (-14 + -5x + x2) = 18 Solving -14 + -5x + x2 = 18 Solving for variable 'x'. Reorder the terms: -14 + -18 + -5x + x2 = 18 + -18 Combine like terms: -14 + -18 = -32 -32 + -5x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -32 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -5x + x2 = 0 + 32 -5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -5x + x2 = 32 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 = 32 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 32 + 6.25 Combine like terms: 32 + 6.25 = 38.25 6.25 + -5x + x2 = 38.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -2.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -2.5 = 6.184658438 Simplifying x + -2.5 = 6.184658438 Reorder the terms: -2.5 + x = 6.184658438 Solving -2.5 + x = 6.184658438 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 = 6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.184658438 + 2.5 x = 6.184658438 + 2.5 Combine like terms: 6.184658438 + 2.5 = 8.684658438 x = 8.684658438 Simplifying x = 8.684658438Subproblem 2
x + -2.5 = -6.184658438 Simplifying x + -2.5 = -6.184658438 Reorder the terms: -2.5 + x = -6.184658438 Solving -2.5 + x = -6.184658438 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 = -6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.184658438 + 2.5 x = -6.184658438 + 2.5 Combine like terms: -6.184658438 + 2.5 = -3.684658438 x = -3.684658438 Simplifying x = -3.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.684658438, -3.684658438}
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