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Simplifying 11x2 + -13x + -17 = 0 Reorder the terms: -17 + -13x + 11x2 = 0 Solving -17 + -13x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.545454545 + -1.181818182x + x2 = 0 Move the constant term to the right: Add '1.545454545' to each side of the equation. -1.545454545 + -1.181818182x + 1.545454545 + x2 = 0 + 1.545454545 Reorder the terms: -1.545454545 + 1.545454545 + -1.181818182x + x2 = 0 + 1.545454545 Combine like terms: -1.545454545 + 1.545454545 = 0.000000000 0.000000000 + -1.181818182x + x2 = 0 + 1.545454545 -1.181818182x + x2 = 0 + 1.545454545 Combine like terms: 0 + 1.545454545 = 1.545454545 -1.181818182x + x2 = 1.545454545 The x term is -1.181818182x. Take half its coefficient (-0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. -1.181818182x + 0.3491735538 + x2 = 1.545454545 + 0.3491735538 Reorder the terms: 0.3491735538 + -1.181818182x + x2 = 1.545454545 + 0.3491735538 Combine like terms: 1.545454545 + 0.3491735538 = 1.8946280988 0.3491735538 + -1.181818182x + x2 = 1.8946280988 Factor a perfect square on the left side: (x + -0.590909091)(x + -0.590909091) = 1.8946280988 Calculate the square root of the right side: 1.376454903 Break this problem into two subproblems by setting (x + -0.590909091) equal to 1.376454903 and -1.376454903.Subproblem 1
x + -0.590909091 = 1.376454903 Simplifying x + -0.590909091 = 1.376454903 Reorder the terms: -0.590909091 + x = 1.376454903 Solving -0.590909091 + x = 1.376454903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = 1.376454903 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = 1.376454903 + 0.590909091 x = 1.376454903 + 0.590909091 Combine like terms: 1.376454903 + 0.590909091 = 1.967363994 x = 1.967363994 Simplifying x = 1.967363994Subproblem 2
x + -0.590909091 = -1.376454903 Simplifying x + -0.590909091 = -1.376454903 Reorder the terms: -0.590909091 + x = -1.376454903 Solving -0.590909091 + x = -1.376454903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = -1.376454903 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = -1.376454903 + 0.590909091 x = -1.376454903 + 0.590909091 Combine like terms: -1.376454903 + 0.590909091 = -0.785545812 x = -0.785545812 Simplifying x = -0.785545812Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.967363994, -0.785545812}
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