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Simplifying x2 + 16x = 250 Reorder the terms: 16x + x2 = 250 Solving 16x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 16x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 16x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 16x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 16x + x2 = 0 + 250 16x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 16x + x2 = 250 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 = 250 + 64 Reorder the terms: 64 + 16x + x2 = 250 + 64 Combine like terms: 250 + 64 = 314 64 + 16x + x2 = 314 Factor a perfect square on the left side: (x + 8)(x + 8) = 314 Calculate the square root of the right side: 17.720045147 Break this problem into two subproblems by setting (x + 8) equal to 17.720045147 and -17.720045147.Subproblem 1
x + 8 = 17.720045147 Simplifying x + 8 = 17.720045147 Reorder the terms: 8 + x = 17.720045147 Solving 8 + x = 17.720045147 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 = 17.720045147 + -8 Combine like terms: 8 + -8 = 0 0 + x = 17.720045147 + -8 x = 17.720045147 + -8 Combine like terms: 17.720045147 + -8 = 9.720045147 x = 9.720045147 Simplifying x = 9.720045147Subproblem 2
x + 8 = -17.720045147 Simplifying x + 8 = -17.720045147 Reorder the terms: 8 + x = -17.720045147 Solving 8 + x = -17.720045147 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 = -17.720045147 + -8 Combine like terms: 8 + -8 = 0 0 + x = -17.720045147 + -8 x = -17.720045147 + -8 Combine like terms: -17.720045147 + -8 = -25.720045147 x = -25.720045147 Simplifying x = -25.720045147Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.720045147, -25.720045147}
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