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Simplifying 6x2 + -3x + -46 = 1594 Reorder the terms: -46 + -3x + 6x2 = 1594 Solving -46 + -3x + 6x2 = 1594 Solving for variable 'x'. Reorder the terms: -46 + -1594 + -3x + 6x2 = 1594 + -1594 Combine like terms: -46 + -1594 = -1640 -1640 + -3x + 6x2 = 1594 + -1594 Combine like terms: 1594 + -1594 = 0 -1640 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -273.3333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '273.3333333' to each side of the equation. -273.3333333 + -0.5x + 273.3333333 + x2 = 0 + 273.3333333 Reorder the terms: -273.3333333 + 273.3333333 + -0.5x + x2 = 0 + 273.3333333 Combine like terms: -273.3333333 + 273.3333333 = 0.0000000 0.0000000 + -0.5x + x2 = 0 + 273.3333333 -0.5x + x2 = 0 + 273.3333333 Combine like terms: 0 + 273.3333333 = 273.3333333 -0.5x + x2 = 273.3333333 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 = 273.3333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 273.3333333 + 0.0625 Combine like terms: 273.3333333 + 0.0625 = 273.3958333 0.0625 + -0.5x + x2 = 273.3958333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 273.3958333 Calculate the square root of the right side: 16.534685764 Break this problem into two subproblems by setting (x + -0.25) equal to 16.534685764 and -16.534685764.Subproblem 1
x + -0.25 = 16.534685764 Simplifying x + -0.25 = 16.534685764 Reorder the terms: -0.25 + x = 16.534685764 Solving -0.25 + x = 16.534685764 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 = 16.534685764 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 16.534685764 + 0.25 x = 16.534685764 + 0.25 Combine like terms: 16.534685764 + 0.25 = 16.784685764 x = 16.784685764 Simplifying x = 16.784685764Subproblem 2
x + -0.25 = -16.534685764 Simplifying x + -0.25 = -16.534685764 Reorder the terms: -0.25 + x = -16.534685764 Solving -0.25 + x = -16.534685764 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 = -16.534685764 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -16.534685764 + 0.25 x = -16.534685764 + 0.25 Combine like terms: -16.534685764 + 0.25 = -16.284685764 x = -16.284685764 Simplifying x = -16.284685764Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.784685764, -16.284685764}
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