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Simplifying x2 + 6x = 44 Reorder the terms: 6x + x2 = 44 Solving 6x + x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 6x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 6x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 6x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 6x + x2 = 0 + 44 6x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 6x + x2 = 44 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 = 44 + 9 Reorder the terms: 9 + 6x + x2 = 44 + 9 Combine like terms: 44 + 9 = 53 9 + 6x + x2 = 53 Factor a perfect square on the left side: (x + 3)(x + 3) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 3) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 3 = 7.280109889 Simplifying x + 3 = 7.280109889 Reorder the terms: 3 + x = 7.280109889 Solving 3 + x = 7.280109889 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 = 7.280109889 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.280109889 + -3 x = 7.280109889 + -3 Combine like terms: 7.280109889 + -3 = 4.280109889 x = 4.280109889 Simplifying x = 4.280109889Subproblem 2
x + 3 = -7.280109889 Simplifying x + 3 = -7.280109889 Reorder the terms: 3 + x = -7.280109889 Solving 3 + x = -7.280109889 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 = -7.280109889 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.280109889 + -3 x = -7.280109889 + -3 Combine like terms: -7.280109889 + -3 = -10.280109889 x = -10.280109889 Simplifying x = -10.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.280109889, -10.280109889}
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