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Simplifying (x + 2)(x + 4) = 10 Reorder the terms: (2 + x)(x + 4) = 10 Reorder the terms: (2 + x)(4 + x) = 10 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 10 ((4 * 2 + x * 2) + x(4 + x)) = 10 ((8 + 2x) + x(4 + x)) = 10 (8 + 2x + (4 * x + x * x)) = 10 (8 + 2x + (4x + x2)) = 10 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 10 Solving 8 + 6x + x2 = 10 Solving for variable 'x'. Reorder the terms: 8 + -10 + 6x + x2 = 10 + -10 Combine like terms: 8 + -10 = -2 -2 + 6x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -2 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6x + x2 = 0 + 2 6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6x + x2 = 2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + 6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6x + x2 = 11 Factor a perfect square on the left side: (x + 3)(x + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479Subproblem 2
x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}
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