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Simplifying x2 + 6x + -68 = 0 Reorder the terms: -68 + 6x + x2 = 0 Solving -68 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 6x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 6x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 6x + x2 = 0 + 68 6x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 6x + x2 = 68 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 = 68 + 9 Reorder the terms: 9 + 6x + x2 = 68 + 9 Combine like terms: 68 + 9 = 77 9 + 6x + x2 = 77 Factor a perfect square on the left side: (x + 3)(x + 3) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 3) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 3 = 8.774964387 Simplifying x + 3 = 8.774964387 Reorder the terms: 3 + x = 8.774964387 Solving 3 + x = 8.774964387 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 = 8.774964387 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.774964387 + -3 x = 8.774964387 + -3 Combine like terms: 8.774964387 + -3 = 5.774964387 x = 5.774964387 Simplifying x = 5.774964387Subproblem 2
x + 3 = -8.774964387 Simplifying x + 3 = -8.774964387 Reorder the terms: 3 + x = -8.774964387 Solving 3 + x = -8.774964387 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 = -8.774964387 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.774964387 + -3 x = -8.774964387 + -3 Combine like terms: -8.774964387 + -3 = -11.774964387 x = -11.774964387 Simplifying x = -11.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.774964387, -11.774964387}
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