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Simplifying (x + 8)(x + -2) = 12 Reorder the terms: (8 + x)(x + -2) = 12 Reorder the terms: (8 + x)(-2 + x) = 12 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = 12 ((-2 * 8 + x * 8) + x(-2 + x)) = 12 ((-16 + 8x) + x(-2 + x)) = 12 (-16 + 8x + (-2 * x + x * x)) = 12 (-16 + 8x + (-2x + x2)) = 12 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = 12 Solving -16 + 6x + x2 = 12 Solving for variable 'x'. Reorder the terms: -16 + -12 + 6x + x2 = 12 + -12 Combine like terms: -16 + -12 = -28 -28 + 6x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -28 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 6x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 6x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 6x + x2 = 0 + 28 6x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 6x + x2 = 28 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 = 28 + 9 Reorder the terms: 9 + 6x + x2 = 28 + 9 Combine like terms: 28 + 9 = 37 9 + 6x + x2 = 37 Factor a perfect square on the left side: (x + 3)(x + 3) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 3) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 3 = 6.08276253 Simplifying x + 3 = 6.08276253 Reorder the terms: 3 + x = 6.08276253 Solving 3 + x = 6.08276253 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 = 6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.08276253 + -3 x = 6.08276253 + -3 Combine like terms: 6.08276253 + -3 = 3.08276253 x = 3.08276253 Simplifying x = 3.08276253Subproblem 2
x + 3 = -6.08276253 Simplifying x + 3 = -6.08276253 Reorder the terms: 3 + x = -6.08276253 Solving 3 + x = -6.08276253 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 = -6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.08276253 + -3 x = -6.08276253 + -3 Combine like terms: -6.08276253 + -3 = -9.08276253 x = -9.08276253 Simplifying x = -9.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.08276253, -9.08276253}
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