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Simplifying 13x2 + 6x + -294.775 = 0 Reorder the terms: -294.775 + 6x + 13x2 = 0 Solving -294.775 + 6x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -22.675 + 0.4615384615x + x2 = 0 Move the constant term to the right: Add '22.675' to each side of the equation. -22.675 + 0.4615384615x + 22.675 + x2 = 0 + 22.675 Reorder the terms: -22.675 + 22.675 + 0.4615384615x + x2 = 0 + 22.675 Combine like terms: -22.675 + 22.675 = 0.000 0.000 + 0.4615384615x + x2 = 0 + 22.675 0.4615384615x + x2 = 0 + 22.675 Combine like terms: 0 + 22.675 = 22.675 0.4615384615x + x2 = 22.675 The x term is 0.4615384615x. Take half its coefficient (0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. 0.4615384615x + 0.05325443788 + x2 = 22.675 + 0.05325443788 Reorder the terms: 0.05325443788 + 0.4615384615x + x2 = 22.675 + 0.05325443788 Combine like terms: 22.675 + 0.05325443788 = 22.72825443788 0.05325443788 + 0.4615384615x + x2 = 22.72825443788 Factor a perfect square on the left side: (x + 0.2307692308)(x + 0.2307692308) = 22.72825443788 Calculate the square root of the right side: 4.767415908 Break this problem into two subproblems by setting (x + 0.2307692308) equal to 4.767415908 and -4.767415908.Subproblem 1
x + 0.2307692308 = 4.767415908 Simplifying x + 0.2307692308 = 4.767415908 Reorder the terms: 0.2307692308 + x = 4.767415908 Solving 0.2307692308 + x = 4.767415908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + x = 4.767415908 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = 4.767415908 + -0.2307692308 x = 4.767415908 + -0.2307692308 Combine like terms: 4.767415908 + -0.2307692308 = 4.5366466772 x = 4.5366466772 Simplifying x = 4.5366466772Subproblem 2
x + 0.2307692308 = -4.767415908 Simplifying x + 0.2307692308 = -4.767415908 Reorder the terms: 0.2307692308 + x = -4.767415908 Solving 0.2307692308 + x = -4.767415908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + x = -4.767415908 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = -4.767415908 + -0.2307692308 x = -4.767415908 + -0.2307692308 Combine like terms: -4.767415908 + -0.2307692308 = -4.9981851388 x = -4.9981851388 Simplifying x = -4.9981851388Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5366466772, -4.9981851388}
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