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Simplifying 13x2 + 6x + -4 = 0 Reorder the terms: -4 + 6x + 13x2 = 0 Solving -4 + 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'. -0.3076923077 + 0.4615384615x + x2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.4615384615x + 0.3076923077 + x2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + 0.4615384615x + x2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + 0.4615384615x + x2 = 0 + 0.3076923077 0.4615384615x + x2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 0.4615384615x + x2 = 0.3076923077 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 = 0.3076923077 + 0.05325443788 Reorder the terms: 0.05325443788 + 0.4615384615x + x2 = 0.3076923077 + 0.05325443788 Combine like terms: 0.3076923077 + 0.05325443788 = 0.36094674558 0.05325443788 + 0.4615384615x + x2 = 0.36094674558 Factor a perfect square on the left side: (x + 0.2307692308)(x + 0.2307692308) = 0.36094674558 Calculate the square root of the right side: 0.600788437 Break this problem into two subproblems by setting (x + 0.2307692308) equal to 0.600788437 and -0.600788437.Subproblem 1
x + 0.2307692308 = 0.600788437 Simplifying x + 0.2307692308 = 0.600788437 Reorder the terms: 0.2307692308 + x = 0.600788437 Solving 0.2307692308 + x = 0.600788437 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 = 0.600788437 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = 0.600788437 + -0.2307692308 x = 0.600788437 + -0.2307692308 Combine like terms: 0.600788437 + -0.2307692308 = 0.3700192062 x = 0.3700192062 Simplifying x = 0.3700192062Subproblem 2
x + 0.2307692308 = -0.600788437 Simplifying x + 0.2307692308 = -0.600788437 Reorder the terms: 0.2307692308 + x = -0.600788437 Solving 0.2307692308 + x = -0.600788437 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 = -0.600788437 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = -0.600788437 + -0.2307692308 x = -0.600788437 + -0.2307692308 Combine like terms: -0.600788437 + -0.2307692308 = -0.8315576678 x = -0.8315576678 Simplifying x = -0.8315576678Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3700192062, -0.8315576678}
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