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Simplifying x2 + 16 = 170 + -1x Reorder the terms: 16 + x2 = 170 + -1x Solving 16 + x2 = 170 + -1x Solving for variable 'x'. Reorder the terms: 16 + -170 + x + x2 = 170 + -1x + -170 + x Combine like terms: 16 + -170 = -154 -154 + x + x2 = 170 + -1x + -170 + x Reorder the terms: -154 + x + x2 = 170 + -170 + -1x + x Combine like terms: 170 + -170 = 0 -154 + x + x2 = 0 + -1x + x -154 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -154 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + x + x2 = 0 + 154 x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 x + x2 = 154 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 154 + 0.25 Reorder the terms: 0.25 + x + x2 = 154 + 0.25 Combine like terms: 154 + 0.25 = 154.25 0.25 + x + x2 = 154.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (x + 0.5) equal to 12.419742348 and -12.419742348.Subproblem 1
x + 0.5 = 12.419742348 Simplifying x + 0.5 = 12.419742348 Reorder the terms: 0.5 + x = 12.419742348 Solving 0.5 + x = 12.419742348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.419742348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.419742348 + -0.5 x = 12.419742348 + -0.5 Combine like terms: 12.419742348 + -0.5 = 11.919742348 x = 11.919742348 Simplifying x = 11.919742348Subproblem 2
x + 0.5 = -12.419742348 Simplifying x + 0.5 = -12.419742348 Reorder the terms: 0.5 + x = -12.419742348 Solving 0.5 + x = -12.419742348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.419742348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.419742348 + -0.5 x = -12.419742348 + -0.5 Combine like terms: -12.419742348 + -0.5 = -12.919742348 x = -12.919742348 Simplifying x = -12.919742348Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.919742348, -12.919742348}
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