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Simplifying x(x + 6) = 192 Reorder the terms: x(6 + x) = 192 (6 * x + x * x) = 192 (6x + x2) = 192 Solving 6x + x2 = 192 Solving for variable 'x'. Reorder the terms: -192 + 6x + x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -192 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 6x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 6x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 6x + x2 = 0 + 192 6x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 6x + x2 = 192 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 = 192 + 9 Reorder the terms: 9 + 6x + x2 = 192 + 9 Combine like terms: 192 + 9 = 201 9 + 6x + x2 = 201 Factor a perfect square on the left side: (x + 3)(x + 3) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + 3) equal to 14.177446879 and -14.177446879.Subproblem 1
x + 3 = 14.177446879 Simplifying x + 3 = 14.177446879 Reorder the terms: 3 + x = 14.177446879 Solving 3 + x = 14.177446879 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 = 14.177446879 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.177446879 + -3 x = 14.177446879 + -3 Combine like terms: 14.177446879 + -3 = 11.177446879 x = 11.177446879 Simplifying x = 11.177446879Subproblem 2
x + 3 = -14.177446879 Simplifying x + 3 = -14.177446879 Reorder the terms: 3 + x = -14.177446879 Solving 3 + x = -14.177446879 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 = -14.177446879 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.177446879 + -3 x = -14.177446879 + -3 Combine like terms: -14.177446879 + -3 = -17.177446879 x = -17.177446879 Simplifying x = -17.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.177446879, -17.177446879}
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