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Simplifying 16x + x2 = 400 Solving 16x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 16x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 16x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 16x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 16x + x2 = 0 + 400 16x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 16x + x2 = 400 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 = 400 + 64 Reorder the terms: 64 + 16x + x2 = 400 + 64 Combine like terms: 400 + 64 = 464 64 + 16x + x2 = 464 Factor a perfect square on the left side: (x + 8)(x + 8) = 464 Calculate the square root of the right side: 21.540659229 Break this problem into two subproblems by setting (x + 8) equal to 21.540659229 and -21.540659229.Subproblem 1
x + 8 = 21.540659229 Simplifying x + 8 = 21.540659229 Reorder the terms: 8 + x = 21.540659229 Solving 8 + x = 21.540659229 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 = 21.540659229 + -8 Combine like terms: 8 + -8 = 0 0 + x = 21.540659229 + -8 x = 21.540659229 + -8 Combine like terms: 21.540659229 + -8 = 13.540659229 x = 13.540659229 Simplifying x = 13.540659229Subproblem 2
x + 8 = -21.540659229 Simplifying x + 8 = -21.540659229 Reorder the terms: 8 + x = -21.540659229 Solving 8 + x = -21.540659229 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 = -21.540659229 + -8 Combine like terms: 8 + -8 = 0 0 + x = -21.540659229 + -8 x = -21.540659229 + -8 Combine like terms: -21.540659229 + -8 = -29.540659229 x = -29.540659229 Simplifying x = -29.540659229Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.540659229, -29.540659229}
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