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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 = 3.830951895 x = 3.830951895 Simplifying x = 3.830951895Subproblem 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 = -7.830951895 x = -7.830951895 Simplifying x = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.830951895, -7.830951895}
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