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Simplifying x2 + -6x + 9 = 91 Reorder the terms: 9 + -6x + x2 = 91 Solving 9 + -6x + x2 = 91 Solving for variable 'x'. Reorder the terms: 9 + -91 + -6x + x2 = 91 + -91 Combine like terms: 9 + -91 = -82 -82 + -6x + x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -82 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -6x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + -6x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -6x + x2 = 0 + 82 -6x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 -6x + x2 = 82 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 = 82 + 9 Reorder the terms: 9 + -6x + x2 = 82 + 9 Combine like terms: 82 + 9 = 91 9 + -6x + x2 = 91 Factor a perfect square on the left side: (x + -3)(x + -3) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -3) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -3 = 9.539392014 Simplifying x + -3 = 9.539392014 Reorder the terms: -3 + x = 9.539392014 Solving -3 + x = 9.539392014 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 = 9.539392014 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.539392014 + 3 x = 9.539392014 + 3 Combine like terms: 9.539392014 + 3 = 12.539392014 x = 12.539392014 Simplifying x = 12.539392014Subproblem 2
x + -3 = -9.539392014 Simplifying x + -3 = -9.539392014 Reorder the terms: -3 + x = -9.539392014 Solving -3 + x = -9.539392014 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 = -9.539392014 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.539392014 + 3 x = -9.539392014 + 3 Combine like terms: -9.539392014 + 3 = -6.539392014 x = -6.539392014 Simplifying x = -6.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.539392014, -6.539392014}
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