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Simplifying 16x + x2 = 300 Solving 16x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 16x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 16x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 16x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 16x + x2 = 0 + 300 16x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 16x + x2 = 300 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 300 + 64 Reorder the terms: 64 + 16x + x2 = 300 + 64 Combine like terms: 300 + 64 = 364 64 + 16x + x2 = 364 Factor a perfect square on the left side: (x + 8)(x + 8) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (x + 8) equal to 19.078784028 and -19.078784028.Subproblem 1
x + 8 = 19.078784028 Simplifying x + 8 = 19.078784028 Reorder the terms: 8 + x = 19.078784028 Solving 8 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 19.078784028 + -8 Combine like terms: 8 + -8 = 0 0 + x = 19.078784028 + -8 x = 19.078784028 + -8 Combine like terms: 19.078784028 + -8 = 11.078784028 x = 11.078784028 Simplifying x = 11.078784028Subproblem 2
x + 8 = -19.078784028 Simplifying x + 8 = -19.078784028 Reorder the terms: 8 + x = -19.078784028 Solving 8 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -19.078784028 + -8 Combine like terms: 8 + -8 = 0 0 + x = -19.078784028 + -8 x = -19.078784028 + -8 Combine like terms: -19.078784028 + -8 = -27.078784028 x = -27.078784028 Simplifying x = -27.078784028Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.078784028, -27.078784028}
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