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Simplifying x2 + 12x + -582 = 0 Reorder the terms: -582 + 12x + x2 = 0 Solving -582 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '582' to each side of the equation. -582 + 12x + 582 + x2 = 0 + 582 Reorder the terms: -582 + 582 + 12x + x2 = 0 + 582 Combine like terms: -582 + 582 = 0 0 + 12x + x2 = 0 + 582 12x + x2 = 0 + 582 Combine like terms: 0 + 582 = 582 12x + x2 = 582 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 = 582 + 36 Reorder the terms: 36 + 12x + x2 = 582 + 36 Combine like terms: 582 + 36 = 618 36 + 12x + x2 = 618 Factor a perfect square on the left side: (x + 6)(x + 6) = 618 Calculate the square root of the right side: 24.859605789 Break this problem into two subproblems by setting (x + 6) equal to 24.859605789 and -24.859605789.Subproblem 1
x + 6 = 24.859605789 Simplifying x + 6 = 24.859605789 Reorder the terms: 6 + x = 24.859605789 Solving 6 + x = 24.859605789 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 = 24.859605789 + -6 Combine like terms: 6 + -6 = 0 0 + x = 24.859605789 + -6 x = 24.859605789 + -6 Combine like terms: 24.859605789 + -6 = 18.859605789 x = 18.859605789 Simplifying x = 18.859605789Subproblem 2
x + 6 = -24.859605789 Simplifying x + 6 = -24.859605789 Reorder the terms: 6 + x = -24.859605789 Solving 6 + x = -24.859605789 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 = -24.859605789 + -6 Combine like terms: 6 + -6 = 0 0 + x = -24.859605789 + -6 x = -24.859605789 + -6 Combine like terms: -24.859605789 + -6 = -30.859605789 x = -30.859605789 Simplifying x = -30.859605789Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.859605789, -30.859605789}
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