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Simplifying 7x2 + -11x + -26 = 0 Reorder the terms: -26 + -11x + 7x2 = 0 Solving -26 + -11x + 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'. -3.714285714 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '3.714285714' to each side of the equation. -3.714285714 + -1.571428571x + 3.714285714 + x2 = 0 + 3.714285714 Reorder the terms: -3.714285714 + 3.714285714 + -1.571428571x + x2 = 0 + 3.714285714 Combine like terms: -3.714285714 + 3.714285714 = 0.000000000 0.000000000 + -1.571428571x + x2 = 0 + 3.714285714 -1.571428571x + x2 = 0 + 3.714285714 Combine like terms: 0 + 3.714285714 = 3.714285714 -1.571428571x + x2 = 3.714285714 The x term is -1.571428571x. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571x + 0.6173469384 + x2 = 3.714285714 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = 3.714285714 + 0.6173469384 Combine like terms: 3.714285714 + 0.6173469384 = 4.3316326524 0.6173469384 + -1.571428571x + x2 = 4.3316326524 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 4.3316326524 Calculate the square root of the right side: 2.081257469 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 2.081257469 and -2.081257469.Subproblem 1
x + -0.7857142855 = 2.081257469 Simplifying x + -0.7857142855 = 2.081257469 Reorder the terms: -0.7857142855 + x = 2.081257469 Solving -0.7857142855 + x = 2.081257469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 2.081257469 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 2.081257469 + 0.7857142855 x = 2.081257469 + 0.7857142855 Combine like terms: 2.081257469 + 0.7857142855 = 2.8669717545 x = 2.8669717545 Simplifying x = 2.8669717545Subproblem 2
x + -0.7857142855 = -2.081257469 Simplifying x + -0.7857142855 = -2.081257469 Reorder the terms: -0.7857142855 + x = -2.081257469 Solving -0.7857142855 + x = -2.081257469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -2.081257469 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -2.081257469 + 0.7857142855 x = -2.081257469 + 0.7857142855 Combine like terms: -2.081257469 + 0.7857142855 = -1.2955431835 x = -1.2955431835 Simplifying x = -1.2955431835Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8669717545, -1.2955431835}
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