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Simplifying x2 + 12x + -419 = 0 Reorder the terms: -419 + 12x + x2 = 0 Solving -419 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '419' to each side of the equation. -419 + 12x + 419 + x2 = 0 + 419 Reorder the terms: -419 + 419 + 12x + x2 = 0 + 419 Combine like terms: -419 + 419 = 0 0 + 12x + x2 = 0 + 419 12x + x2 = 0 + 419 Combine like terms: 0 + 419 = 419 12x + x2 = 419 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 = 419 + 36 Reorder the terms: 36 + 12x + x2 = 419 + 36 Combine like terms: 419 + 36 = 455 36 + 12x + x2 = 455 Factor a perfect square on the left side: (x + 6)(x + 6) = 455 Calculate the square root of the right side: 21.330729008 Break this problem into two subproblems by setting (x + 6) equal to 21.330729008 and -21.330729008.Subproblem 1
x + 6 = 21.330729008 Simplifying x + 6 = 21.330729008 Reorder the terms: 6 + x = 21.330729008 Solving 6 + x = 21.330729008 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 = 21.330729008 + -6 Combine like terms: 6 + -6 = 0 0 + x = 21.330729008 + -6 x = 21.330729008 + -6 Combine like terms: 21.330729008 + -6 = 15.330729008 x = 15.330729008 Simplifying x = 15.330729008Subproblem 2
x + 6 = -21.330729008 Simplifying x + 6 = -21.330729008 Reorder the terms: 6 + x = -21.330729008 Solving 6 + x = -21.330729008 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 = -21.330729008 + -6 Combine like terms: 6 + -6 = 0 0 + x = -21.330729008 + -6 x = -21.330729008 + -6 Combine like terms: -21.330729008 + -6 = -27.330729008 x = -27.330729008 Simplifying x = -27.330729008Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.330729008, -27.330729008}
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