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Simplifying x2 + -6x + -272 = 0 Reorder the terms: -272 + -6x + x2 = 0 Solving -272 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '272' to each side of the equation. -272 + -6x + 272 + x2 = 0 + 272 Reorder the terms: -272 + 272 + -6x + x2 = 0 + 272 Combine like terms: -272 + 272 = 0 0 + -6x + x2 = 0 + 272 -6x + x2 = 0 + 272 Combine like terms: 0 + 272 = 272 -6x + x2 = 272 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 = 272 + 9 Reorder the terms: 9 + -6x + x2 = 272 + 9 Combine like terms: 272 + 9 = 281 9 + -6x + x2 = 281 Factor a perfect square on the left side: (x + -3)(x + -3) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + -3) equal to 16.763054614 and -16.763054614.Subproblem 1
x + -3 = 16.763054614 Simplifying x + -3 = 16.763054614 Reorder the terms: -3 + x = 16.763054614 Solving -3 + x = 16.763054614 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 = 16.763054614 + 3 Combine like terms: -3 + 3 = 0 0 + x = 16.763054614 + 3 x = 16.763054614 + 3 Combine like terms: 16.763054614 + 3 = 19.763054614 x = 19.763054614 Simplifying x = 19.763054614Subproblem 2
x + -3 = -16.763054614 Simplifying x + -3 = -16.763054614 Reorder the terms: -3 + x = -16.763054614 Solving -3 + x = -16.763054614 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 = -16.763054614 + 3 Combine like terms: -3 + 3 = 0 0 + x = -16.763054614 + 3 x = -16.763054614 + 3 Combine like terms: -16.763054614 + 3 = -13.763054614 x = -13.763054614 Simplifying x = -13.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.763054614, -13.763054614}
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