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Simplifying x2 + -6x + -81 = 90 Reorder the terms: -81 + -6x + x2 = 90 Solving -81 + -6x + x2 = 90 Solving for variable 'x'. Reorder the terms: -81 + -90 + -6x + x2 = 90 + -90 Combine like terms: -81 + -90 = -171 -171 + -6x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -171 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + -6x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + -6x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + -6x + x2 = 0 + 171 -6x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 -6x + x2 = 171 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 = 171 + 9 Reorder the terms: 9 + -6x + x2 = 171 + 9 Combine like terms: 171 + 9 = 180 9 + -6x + x2 = 180 Factor a perfect square on the left side: (x + -3)(x + -3) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -3) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -3 = 13.416407865 Simplifying x + -3 = 13.416407865 Reorder the terms: -3 + x = 13.416407865 Solving -3 + x = 13.416407865 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 = 13.416407865 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.416407865 + 3 x = 13.416407865 + 3 Combine like terms: 13.416407865 + 3 = 16.416407865 x = 16.416407865 Simplifying x = 16.416407865Subproblem 2
x + -3 = -13.416407865 Simplifying x + -3 = -13.416407865 Reorder the terms: -3 + x = -13.416407865 Solving -3 + x = -13.416407865 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 = -13.416407865 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.416407865 + 3 x = -13.416407865 + 3 Combine like terms: -13.416407865 + 3 = -10.416407865 x = -10.416407865 Simplifying x = -10.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.416407865, -10.416407865}
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