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Simplifying 22 = x2 + 6x Reorder the terms: 22 = 6x + x2 Solving 22 = 6x + x2 Solving for variable 'x'. Reorder the terms: 22 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 22 + -6x + -1x2 = 0 + x2 + -1x2 22 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + 6x + x2 = 0 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 = 2.567764363 x = 2.567764363 Simplifying x = 2.567764363Subproblem 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 = -8.567764363 x = -8.567764363 Simplifying x = -8.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.567764363, -8.567764363}
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