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Simplifying x(x + 12) = 202 Reorder the terms: x(12 + x) = 202 (12 * x + x * x) = 202 (12x + x2) = 202 Solving 12x + x2 = 202 Solving for variable 'x'. Reorder the terms: -202 + 12x + x2 = 202 + -202 Combine like terms: 202 + -202 = 0 -202 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '202' to each side of the equation. -202 + 12x + 202 + x2 = 0 + 202 Reorder the terms: -202 + 202 + 12x + x2 = 0 + 202 Combine like terms: -202 + 202 = 0 0 + 12x + x2 = 0 + 202 12x + x2 = 0 + 202 Combine like terms: 0 + 202 = 202 12x + x2 = 202 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 202 + 36 Reorder the terms: 36 + 12x + x2 = 202 + 36 Combine like terms: 202 + 36 = 238 36 + 12x + x2 = 238 Factor a perfect square on the left side: (x + 6)(x + 6) = 238 Calculate the square root of the right side: 15.427248621 Break this problem into two subproblems by setting (x + 6) equal to 15.427248621 and -15.427248621.Subproblem 1
x + 6 = 15.427248621 Simplifying x + 6 = 15.427248621 Reorder the terms: 6 + x = 15.427248621 Solving 6 + x = 15.427248621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 15.427248621 + -6 Combine like terms: 6 + -6 = 0 0 + x = 15.427248621 + -6 x = 15.427248621 + -6 Combine like terms: 15.427248621 + -6 = 9.427248621 x = 9.427248621 Simplifying x = 9.427248621Subproblem 2
x + 6 = -15.427248621 Simplifying x + 6 = -15.427248621 Reorder the terms: 6 + x = -15.427248621 Solving 6 + x = -15.427248621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -15.427248621 + -6 Combine like terms: 6 + -6 = 0 0 + x = -15.427248621 + -6 x = -15.427248621 + -6 Combine like terms: -15.427248621 + -6 = -21.427248621 x = -21.427248621 Simplifying x = -21.427248621Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.427248621, -21.427248621}
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