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Simplifying (x + 3)(x + -7) = 9 Reorder the terms: (3 + x)(x + -7) = 9 Reorder the terms: (3 + x)(-7 + x) = 9 Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) = 9 ((-7 * 3 + x * 3) + x(-7 + x)) = 9 ((-21 + 3x) + x(-7 + x)) = 9 (-21 + 3x + (-7 * x + x * x)) = 9 (-21 + 3x + (-7x + x2)) = 9 Combine like terms: 3x + -7x = -4x (-21 + -4x + x2) = 9 Solving -21 + -4x + x2 = 9 Solving for variable 'x'. Reorder the terms: -21 + -9 + -4x + x2 = 9 + -9 Combine like terms: -21 + -9 = -30 -30 + -4x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -30 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4x + x2 = 0 + 30 -4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4x + x2 = 30 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 30 + 4 Reorder the terms: 4 + -4x + x2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + -4x + x2 = 34 Factor a perfect square on the left side: (x + -2)(x + -2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -2) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -2 = 5.830951895 Simplifying x + -2 = 5.830951895 Reorder the terms: -2 + x = 5.830951895 Solving -2 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.830951895 + 2 x = 5.830951895 + 2 Combine like terms: 5.830951895 + 2 = 7.830951895 x = 7.830951895 Simplifying x = 7.830951895Subproblem 2
x + -2 = -5.830951895 Simplifying x + -2 = -5.830951895 Reorder the terms: -2 + x = -5.830951895 Solving -2 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.830951895 + 2 x = -5.830951895 + 2 Combine like terms: -5.830951895 + 2 = -3.830951895 x = -3.830951895 Simplifying x = -3.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.830951895, -3.830951895}
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