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Simplifying (x + -3)(x + -4) = 27 Reorder the terms: (-3 + x)(x + -4) = 27 Reorder the terms: (-3 + x)(-4 + x) = 27 Multiply (-3 + x) * (-4 + x) (-3(-4 + x) + x(-4 + x)) = 27 ((-4 * -3 + x * -3) + x(-4 + x)) = 27 ((12 + -3x) + x(-4 + x)) = 27 (12 + -3x + (-4 * x + x * x)) = 27 (12 + -3x + (-4x + x2)) = 27 Combine like terms: -3x + -4x = -7x (12 + -7x + x2) = 27 Solving 12 + -7x + x2 = 27 Solving for variable 'x'. Reorder the terms: 12 + -27 + -7x + x2 = 27 + -27 Combine like terms: 12 + -27 = -15 -15 + -7x + x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -15 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -7x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -7x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -7x + x2 = 0 + 15 -7x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -7x + x2 = 15 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 15 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + -7x + x2 = 27.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -3.5 = 5.220153254 Simplifying x + -3.5 = 5.220153254 Reorder the terms: -3.5 + x = 5.220153254 Solving -3.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.220153254 + 3.5 x = 5.220153254 + 3.5 Combine like terms: 5.220153254 + 3.5 = 8.720153254 x = 8.720153254 Simplifying x = 8.720153254Subproblem 2
x + -3.5 = -5.220153254 Simplifying x + -3.5 = -5.220153254 Reorder the terms: -3.5 + x = -5.220153254 Solving -3.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.220153254 + 3.5 x = -5.220153254 + 3.5 Combine like terms: -5.220153254 + 3.5 = -1.720153254 x = -1.720153254 Simplifying x = -1.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.720153254, -1.720153254}
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