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Simplifying x2 + -6x + 9 = 31 Reorder the terms: 9 + -6x + x2 = 31 Solving 9 + -6x + x2 = 31 Solving for variable 'x'. Reorder the terms: 9 + -31 + -6x + x2 = 31 + -31 Combine like terms: 9 + -31 = -22 -22 + -6x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -22 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -6x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -6x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -6x + x2 = 0 + 22 -6x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -6x + x2 = 22 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 = 22 + 9 Reorder the terms: 9 + -6x + x2 = 22 + 9 Combine like terms: 22 + 9 = 31 9 + -6x + x2 = 31 Factor a perfect square on the left side: (x + -3)(x + -3) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -3) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -3 = 5.567764363 Simplifying x + -3 = 5.567764363 Reorder the terms: -3 + x = 5.567764363 Solving -3 + x = 5.567764363 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 = 5.567764363 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.567764363 + 3 x = 5.567764363 + 3 Combine like terms: 5.567764363 + 3 = 8.567764363 x = 8.567764363 Simplifying x = 8.567764363Subproblem 2
x + -3 = -5.567764363 Simplifying x + -3 = -5.567764363 Reorder the terms: -3 + x = -5.567764363 Solving -3 + x = -5.567764363 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 = -5.567764363 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.567764363 + 3 x = -5.567764363 + 3 Combine like terms: -5.567764363 + 3 = -2.567764363 x = -2.567764363 Simplifying x = -2.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.567764363, -2.567764363}
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