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Simplifying 11x2 = 14x + 6 Reorder the terms: 11x2 = 6 + 14x Solving 11x2 = 6 + 14x Solving for variable 'x'. Reorder the terms: -6 + -14x + 11x2 = 6 + 14x + -6 + -14x Reorder the terms: -6 + -14x + 11x2 = 6 + -6 + 14x + -14x Combine like terms: 6 + -6 = 0 -6 + -14x + 11x2 = 0 + 14x + -14x -6 + -14x + 11x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -6 + -14x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + -1.272727273x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -1.272727273x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -1.272727273x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -1.272727273x + x2 = 0 + 0.5454545455 -1.272727273x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -1.272727273x + x2 = 0.5454545455 The x term is -1.272727273x. Take half its coefficient (-0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. -1.272727273x + 0.4049586779 + x2 = 0.5454545455 + 0.4049586779 Reorder the terms: 0.4049586779 + -1.272727273x + x2 = 0.5454545455 + 0.4049586779 Combine like terms: 0.5454545455 + 0.4049586779 = 0.9504132234 0.4049586779 + -1.272727273x + x2 = 0.9504132234 Factor a perfect square on the left side: (x + -0.6363636365)(x + -0.6363636365) = 0.9504132234 Calculate the square root of the right side: 0.974891391 Break this problem into two subproblems by setting (x + -0.6363636365) equal to 0.974891391 and -0.974891391.Subproblem 1
x + -0.6363636365 = 0.974891391 Simplifying x + -0.6363636365 = 0.974891391 Reorder the terms: -0.6363636365 + x = 0.974891391 Solving -0.6363636365 + x = 0.974891391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6363636365' to each side of the equation. -0.6363636365 + 0.6363636365 + x = 0.974891391 + 0.6363636365 Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000 0.0000000000 + x = 0.974891391 + 0.6363636365 x = 0.974891391 + 0.6363636365 Combine like terms: 0.974891391 + 0.6363636365 = 1.6112550275 x = 1.6112550275 Simplifying x = 1.6112550275Subproblem 2
x + -0.6363636365 = -0.974891391 Simplifying x + -0.6363636365 = -0.974891391 Reorder the terms: -0.6363636365 + x = -0.974891391 Solving -0.6363636365 + x = -0.974891391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6363636365' to each side of the equation. -0.6363636365 + 0.6363636365 + x = -0.974891391 + 0.6363636365 Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000 0.0000000000 + x = -0.974891391 + 0.6363636365 x = -0.974891391 + 0.6363636365 Combine like terms: -0.974891391 + 0.6363636365 = -0.3385277545 x = -0.3385277545 Simplifying x = -0.3385277545Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6112550275, -0.3385277545}
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