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Simplifying 7x2 + 14x + -6 = 0 Reorder the terms: -6 + 14x + 7x2 = 0 Solving -6 + 14x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 2x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 2x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 2x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.8571428571 2x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 2x + x2 = 0.8571428571 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.8571428571 + 1 Reorder the terms: 1 + 2x + x2 = 0.8571428571 + 1 Combine like terms: 0.8571428571 + 1 = 1.8571428571 1 + 2x + x2 = 1.8571428571 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.8571428571 Calculate the square root of the right side: 1.362770288 Break this problem into two subproblems by setting (x + 1) equal to 1.362770288 and -1.362770288.Subproblem 1
x + 1 = 1.362770288 Simplifying x + 1 = 1.362770288 Reorder the terms: 1 + x = 1.362770288 Solving 1 + x = 1.362770288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.362770288 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.362770288 + -1 x = 1.362770288 + -1 Combine like terms: 1.362770288 + -1 = 0.362770288 x = 0.362770288 Simplifying x = 0.362770288Subproblem 2
x + 1 = -1.362770288 Simplifying x + 1 = -1.362770288 Reorder the terms: 1 + x = -1.362770288 Solving 1 + x = -1.362770288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.362770288 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.362770288 + -1 x = -1.362770288 + -1 Combine like terms: -1.362770288 + -1 = -2.362770288 x = -2.362770288 Simplifying x = -2.362770288Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.362770288, -2.362770288}
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