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Simplifying x2 + -6x + 7 = 180 Reorder the terms: 7 + -6x + x2 = 180 Solving 7 + -6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 7 + -180 + -6x + x2 = 180 + -180 Combine like terms: 7 + -180 = -173 -173 + -6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -173 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '173' to each side of the equation. -173 + -6x + 173 + x2 = 0 + 173 Reorder the terms: -173 + 173 + -6x + x2 = 0 + 173 Combine like terms: -173 + 173 = 0 0 + -6x + x2 = 0 + 173 -6x + x2 = 0 + 173 Combine like terms: 0 + 173 = 173 -6x + x2 = 173 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 173 + 9 Reorder the terms: 9 + -6x + x2 = 173 + 9 Combine like terms: 173 + 9 = 182 9 + -6x + x2 = 182 Factor a perfect square on the left side: (x + -3)(x + -3) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + -3) equal to 13.490737563 and -13.490737563.Subproblem 1
x + -3 = 13.490737563 Simplifying x + -3 = 13.490737563 Reorder the terms: -3 + x = 13.490737563 Solving -3 + x = 13.490737563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 13.490737563 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.490737563 + 3 x = 13.490737563 + 3 Combine like terms: 13.490737563 + 3 = 16.490737563 x = 16.490737563 Simplifying x = 16.490737563Subproblem 2
x + -3 = -13.490737563 Simplifying x + -3 = -13.490737563 Reorder the terms: -3 + x = -13.490737563 Solving -3 + x = -13.490737563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -13.490737563 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.490737563 + 3 x = -13.490737563 + 3 Combine like terms: -13.490737563 + 3 = -10.490737563 x = -10.490737563 Simplifying x = -10.490737563Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.490737563, -10.490737563}
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