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Simplifying x2 + 12x + -65 = 0 Reorder the terms: -65 + 12x + x2 = 0 Solving -65 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 12x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 12x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 12x + x2 = 0 + 65 12x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 12x + x2 = 65 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 65 + 36 Reorder the terms: 36 + 12x + x2 = 65 + 36 Combine like terms: 65 + 36 = 101 36 + 12x + x2 = 101 Factor a perfect square on the left side: (x + 6)(x + 6) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 6) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 6 = 10.049875621 Simplifying x + 6 = 10.049875621 Reorder the terms: 6 + x = 10.049875621 Solving 6 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 10.049875621 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.049875621 + -6 x = 10.049875621 + -6 Combine like terms: 10.049875621 + -6 = 4.049875621 x = 4.049875621 Simplifying x = 4.049875621Subproblem 2
x + 6 = -10.049875621 Simplifying x + 6 = -10.049875621 Reorder the terms: 6 + x = -10.049875621 Solving 6 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -10.049875621 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.049875621 + -6 x = -10.049875621 + -6 Combine like terms: -10.049875621 + -6 = -16.049875621 x = -16.049875621 Simplifying x = -16.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049875621, -16.049875621}
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