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Simplifying x2 + 9x = 170 Reorder the terms: 9x + x2 = 170 Solving 9x + x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + 9x + x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 9x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 9x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 9x + x2 = 0 + 170 9x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 9x + x2 = 170 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 170 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 170 + 20.25 Combine like terms: 170 + 20.25 = 190.25 20.25 + 9x + x2 = 190.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 4.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 4.5 = 13.793114224 Simplifying x + 4.5 = 13.793114224 Reorder the terms: 4.5 + x = 13.793114224 Solving 4.5 + x = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 13.793114224 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 13.793114224 + -4.5 x = 13.793114224 + -4.5 Combine like terms: 13.793114224 + -4.5 = 9.293114224 x = 9.293114224 Simplifying x = 9.293114224Subproblem 2
x + 4.5 = -13.793114224 Simplifying x + 4.5 = -13.793114224 Reorder the terms: 4.5 + x = -13.793114224 Solving 4.5 + x = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -13.793114224 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -13.793114224 + -4.5 x = -13.793114224 + -4.5 Combine like terms: -13.793114224 + -4.5 = -18.293114224 x = -18.293114224 Simplifying x = -18.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.293114224, -18.293114224}
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