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Simplifying x2 + 12x + -79 = 0 Reorder the terms: -79 + 12x + x2 = 0 Solving -79 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + 12x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + 12x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + 12x + x2 = 0 + 79 12x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 12x + x2 = 79 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 = 79 + 36 Reorder the terms: 36 + 12x + x2 = 79 + 36 Combine like terms: 79 + 36 = 115 36 + 12x + x2 = 115 Factor a perfect square on the left side: (x + 6)(x + 6) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 6) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 6 = 10.723805295 Simplifying x + 6 = 10.723805295 Reorder the terms: 6 + x = 10.723805295 Solving 6 + x = 10.723805295 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 = 10.723805295 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.723805295 + -6 x = 10.723805295 + -6 Combine like terms: 10.723805295 + -6 = 4.723805295 x = 4.723805295 Simplifying x = 4.723805295Subproblem 2
x + 6 = -10.723805295 Simplifying x + 6 = -10.723805295 Reorder the terms: 6 + x = -10.723805295 Solving 6 + x = -10.723805295 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 = -10.723805295 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.723805295 + -6 x = -10.723805295 + -6 Combine like terms: -10.723805295 + -6 = -16.723805295 x = -16.723805295 Simplifying x = -16.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.723805295, -16.723805295}
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