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Simplifying (x + 7)(x + -9) = (3x + -18) Reorder the terms: (7 + x)(x + -9) = (3x + -18) Reorder the terms: (7 + x)(-9 + x) = (3x + -18) Multiply (7 + x) * (-9 + x) (7(-9 + x) + x(-9 + x)) = (3x + -18) ((-9 * 7 + x * 7) + x(-9 + x)) = (3x + -18) ((-63 + 7x) + x(-9 + x)) = (3x + -18) (-63 + 7x + (-9 * x + x * x)) = (3x + -18) (-63 + 7x + (-9x + x2)) = (3x + -18) Combine like terms: 7x + -9x = -2x (-63 + -2x + x2) = (3x + -18) Reorder the terms: -63 + -2x + x2 = (-18 + 3x) Remove parenthesis around (-18 + 3x) -63 + -2x + x2 = -18 + 3x Solving -63 + -2x + x2 = -18 + 3x Solving for variable 'x'. Reorder the terms: -63 + 18 + -2x + -3x + x2 = -18 + 3x + 18 + -3x Combine like terms: -63 + 18 = -45 -45 + -2x + -3x + x2 = -18 + 3x + 18 + -3x Combine like terms: -2x + -3x = -5x -45 + -5x + x2 = -18 + 3x + 18 + -3x Reorder the terms: -45 + -5x + x2 = -18 + 18 + 3x + -3x Combine like terms: -18 + 18 = 0 -45 + -5x + x2 = 0 + 3x + -3x -45 + -5x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -45 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -5x + x2 = 0 + 45 -5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -5x + x2 = 45 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 = 45 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 45 + 6.25 Combine like terms: 45 + 6.25 = 51.25 6.25 + -5x + x2 = 51.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -2.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -2.5 = 7.158910532 Simplifying x + -2.5 = 7.158910532 Reorder the terms: -2.5 + x = 7.158910532 Solving -2.5 + x = 7.158910532 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 = 7.158910532 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.158910532 + 2.5 x = 7.158910532 + 2.5 Combine like terms: 7.158910532 + 2.5 = 9.658910532 x = 9.658910532 Simplifying x = 9.658910532Subproblem 2
x + -2.5 = -7.158910532 Simplifying x + -2.5 = -7.158910532 Reorder the terms: -2.5 + x = -7.158910532 Solving -2.5 + x = -7.158910532 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 = -7.158910532 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.158910532 + 2.5 x = -7.158910532 + 2.5 Combine like terms: -7.158910532 + 2.5 = -4.658910532 x = -4.658910532 Simplifying x = -4.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.658910532, -4.658910532}
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