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Simplifying 7x2 + -13x + -11 = 0 Reorder the terms: -11 + -13x + 7x2 = 0 Solving -11 + -13x + 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'. -1.571428571 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -1.857142857x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -1.857142857x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -1.857142857x + x2 = 0 + 1.571428571 -1.857142857x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -1.857142857x + x2 = 1.571428571 The x term is -1.857142857x. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857x + 0.8622448978 + x2 = 1.571428571 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 1.571428571 + 0.8622448978 Combine like terms: 1.571428571 + 0.8622448978 = 2.4336734688 0.8622448978 + -1.857142857x + x2 = 2.4336734688 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 2.4336734688 Calculate the square root of the right side: 1.560023548 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 1.560023548 and -1.560023548.Subproblem 1
x + -0.9285714285 = 1.560023548 Simplifying x + -0.9285714285 = 1.560023548 Reorder the terms: -0.9285714285 + x = 1.560023548 Solving -0.9285714285 + x = 1.560023548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = 1.560023548 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.560023548 + 0.9285714285 x = 1.560023548 + 0.9285714285 Combine like terms: 1.560023548 + 0.9285714285 = 2.4885949765 x = 2.4885949765 Simplifying x = 2.4885949765Subproblem 2
x + -0.9285714285 = -1.560023548 Simplifying x + -0.9285714285 = -1.560023548 Reorder the terms: -0.9285714285 + x = -1.560023548 Solving -0.9285714285 + x = -1.560023548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = -1.560023548 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.560023548 + 0.9285714285 x = -1.560023548 + 0.9285714285 Combine like terms: -1.560023548 + 0.9285714285 = -0.6314521195 x = -0.6314521195 Simplifying x = -0.6314521195Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4885949765, -0.6314521195}
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