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Simplifying (x + -7)(x + 3) = 4 Reorder the terms: (-7 + x)(x + 3) = 4 Reorder the terms: (-7 + x)(3 + x) = 4 Multiply (-7 + x) * (3 + x) (-7(3 + x) + x(3 + x)) = 4 ((3 * -7 + x * -7) + x(3 + x)) = 4 ((-21 + -7x) + x(3 + x)) = 4 (-21 + -7x + (3 * x + x * x)) = 4 (-21 + -7x + (3x + x2)) = 4 Combine like terms: -7x + 3x = -4x (-21 + -4x + x2) = 4 Solving -21 + -4x + x2 = 4 Solving for variable 'x'. Reorder the terms: -21 + -4 + -4x + x2 = 4 + -4 Combine like terms: -21 + -4 = -25 -25 + -4x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -25 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -4x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -4x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4x + x2 = 0 + 25 -4x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4x + x2 = 25 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 = 25 + 4 Reorder the terms: 4 + -4x + x2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4x + x2 = 29 Factor a perfect square on the left side: (x + -2)(x + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -2 = 5.385164807 Simplifying x + -2 = 5.385164807 Reorder the terms: -2 + x = 5.385164807 Solving -2 + x = 5.385164807 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 = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.385164807 + 2 x = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 x = 7.385164807 Simplifying x = 7.385164807Subproblem 2
x + -2 = -5.385164807 Simplifying x + -2 = -5.385164807 Reorder the terms: -2 + x = -5.385164807 Solving -2 + x = -5.385164807 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 = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.385164807 + 2 x = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 x = -3.385164807 Simplifying x = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.385164807, -3.385164807}
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