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Simplifying x2 + 16x = 346 Reorder the terms: 16x + x2 = 346 Solving 16x + x2 = 346 Solving for variable 'x'. Reorder the terms: -346 + 16x + x2 = 346 + -346 Combine like terms: 346 + -346 = 0 -346 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '346' to each side of the equation. -346 + 16x + 346 + x2 = 0 + 346 Reorder the terms: -346 + 346 + 16x + x2 = 0 + 346 Combine like terms: -346 + 346 = 0 0 + 16x + x2 = 0 + 346 16x + x2 = 0 + 346 Combine like terms: 0 + 346 = 346 16x + x2 = 346 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 = 346 + 64 Reorder the terms: 64 + 16x + x2 = 346 + 64 Combine like terms: 346 + 64 = 410 64 + 16x + x2 = 410 Factor a perfect square on the left side: (x + 8)(x + 8) = 410 Calculate the square root of the right side: 20.248456731 Break this problem into two subproblems by setting (x + 8) equal to 20.248456731 and -20.248456731.Subproblem 1
x + 8 = 20.248456731 Simplifying x + 8 = 20.248456731 Reorder the terms: 8 + x = 20.248456731 Solving 8 + x = 20.248456731 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 = 20.248456731 + -8 Combine like terms: 8 + -8 = 0 0 + x = 20.248456731 + -8 x = 20.248456731 + -8 Combine like terms: 20.248456731 + -8 = 12.248456731 x = 12.248456731 Simplifying x = 12.248456731Subproblem 2
x + 8 = -20.248456731 Simplifying x + 8 = -20.248456731 Reorder the terms: 8 + x = -20.248456731 Solving 8 + x = -20.248456731 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 = -20.248456731 + -8 Combine like terms: 8 + -8 = 0 0 + x = -20.248456731 + -8 x = -20.248456731 + -8 Combine like terms: -20.248456731 + -8 = -28.248456731 x = -28.248456731 Simplifying x = -28.248456731Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.248456731, -28.248456731}
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