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Simplifying (x + 16)(x + 6) = 192 Reorder the terms: (16 + x)(x + 6) = 192 Reorder the terms: (16 + x)(6 + x) = 192 Multiply (16 + x) * (6 + x) (16(6 + x) + x(6 + x)) = 192 ((6 * 16 + x * 16) + x(6 + x)) = 192 ((96 + 16x) + x(6 + x)) = 192 (96 + 16x + (6 * x + x * x)) = 192 (96 + 16x + (6x + x2)) = 192 Combine like terms: 16x + 6x = 22x (96 + 22x + x2) = 192 Solving 96 + 22x + x2 = 192 Solving for variable 'x'. Reorder the terms: 96 + -192 + 22x + x2 = 192 + -192 Combine like terms: 96 + -192 = -96 -96 + 22x + x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -96 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 22x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 22x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 22x + x2 = 0 + 96 22x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 22x + x2 = 96 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 96 + 121 Reorder the terms: 121 + 22x + x2 = 96 + 121 Combine like terms: 96 + 121 = 217 121 + 22x + x2 = 217 Factor a perfect square on the left side: (x + 11)(x + 11) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 11) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 11 = 14.730919863 Simplifying x + 11 = 14.730919863 Reorder the terms: 11 + x = 14.730919863 Solving 11 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 14.730919863 + -11 Combine like terms: 11 + -11 = 0 0 + x = 14.730919863 + -11 x = 14.730919863 + -11 Combine like terms: 14.730919863 + -11 = 3.730919863 x = 3.730919863 Simplifying x = 3.730919863Subproblem 2
x + 11 = -14.730919863 Simplifying x + 11 = -14.730919863 Reorder the terms: 11 + x = -14.730919863 Solving 11 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -14.730919863 + -11 Combine like terms: 11 + -11 = 0 0 + x = -14.730919863 + -11 x = -14.730919863 + -11 Combine like terms: -14.730919863 + -11 = -25.730919863 x = -25.730919863 Simplifying x = -25.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.730919863, -25.730919863}
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