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Simplifying (x + 8)(x + -2) = 21 Reorder the terms: (8 + x)(x + -2) = 21 Reorder the terms: (8 + x)(-2 + x) = 21 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = 21 ((-2 * 8 + x * 8) + x(-2 + x)) = 21 ((-16 + 8x) + x(-2 + x)) = 21 (-16 + 8x + (-2 * x + x * x)) = 21 (-16 + 8x + (-2x + x2)) = 21 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = 21 Solving -16 + 6x + x2 = 21 Solving for variable 'x'. Reorder the terms: -16 + -21 + 6x + x2 = 21 + -21 Combine like terms: -16 + -21 = -37 -37 + 6x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -37 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 6x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 6x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 6x + x2 = 0 + 37 6x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 6x + x2 = 37 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 = 37 + 9 Reorder the terms: 9 + 6x + x2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + 6x + x2 = 46 Factor a perfect square on the left side: (x + 3)(x + 3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 3) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 3 = 6.782329983 Simplifying x + 3 = 6.782329983 Reorder the terms: 3 + x = 6.782329983 Solving 3 + x = 6.782329983 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 = 6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.782329983 + -3 x = 6.782329983 + -3 Combine like terms: 6.782329983 + -3 = 3.782329983 x = 3.782329983 Simplifying x = 3.782329983Subproblem 2
x + 3 = -6.782329983 Simplifying x + 3 = -6.782329983 Reorder the terms: 3 + x = -6.782329983 Solving 3 + x = -6.782329983 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 = -6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.782329983 + -3 x = -6.782329983 + -3 Combine like terms: -6.782329983 + -3 = -9.782329983 x = -9.782329983 Simplifying x = -9.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.782329983, -9.782329983}
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