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Simplifying 0 = 12x2 + -6x + -294.775 Reorder the terms: 0 = -294.775 + -6x + 12x2 Solving 0 = -294.775 + -6x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 294.775 = 294.775 294.775 + 6x + -12x2 = -294.775 + -6x + 12x2 + 294.775 + 6x + -12x2 Reorder the terms: 294.775 + 6x + -12x2 = -294.775 + 294.775 + -6x + 6x + 12x2 + -12x2 Combine like terms: -294.775 + 294.775 = 0.000 294.775 + 6x + -12x2 = 0.000 + -6x + 6x + 12x2 + -12x2 294.775 + 6x + -12x2 = -6x + 6x + 12x2 + -12x2 Combine like terms: -6x + 6x = 0 294.775 + 6x + -12x2 = 0 + 12x2 + -12x2 294.775 + 6x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 294.775 + 6x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -24.56458333 + -0.5x + x2 = 0 Move the constant term to the right: Add '24.56458333' to each side of the equation. -24.56458333 + -0.5x + 24.56458333 + x2 = 0 + 24.56458333 Reorder the terms: -24.56458333 + 24.56458333 + -0.5x + x2 = 0 + 24.56458333 Combine like terms: -24.56458333 + 24.56458333 = 0.00000000 0.00000000 + -0.5x + x2 = 0 + 24.56458333 -0.5x + x2 = 0 + 24.56458333 Combine like terms: 0 + 24.56458333 = 24.56458333 -0.5x + x2 = 24.56458333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 24.56458333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 24.56458333 + 0.0625 Combine like terms: 24.56458333 + 0.0625 = 24.62708333 0.0625 + -0.5x + x2 = 24.62708333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 24.62708333 Calculate the square root of the right side: 4.962568219 Break this problem into two subproblems by setting (x + -0.25) equal to 4.962568219 and -4.962568219.Subproblem 1
x + -0.25 = 4.962568219 Simplifying x + -0.25 = 4.962568219 Reorder the terms: -0.25 + x = 4.962568219 Solving -0.25 + x = 4.962568219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.962568219 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.962568219 + 0.25 x = 4.962568219 + 0.25 Combine like terms: 4.962568219 + 0.25 = 5.212568219 x = 5.212568219 Simplifying x = 5.212568219Subproblem 2
x + -0.25 = -4.962568219 Simplifying x + -0.25 = -4.962568219 Reorder the terms: -0.25 + x = -4.962568219 Solving -0.25 + x = -4.962568219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.962568219 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.962568219 + 0.25 x = -4.962568219 + 0.25 Combine like terms: -4.962568219 + 0.25 = -4.712568219 x = -4.712568219 Simplifying x = -4.712568219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.212568219, -4.712568219}
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