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Simplifying 11x2 + 13x + -72 = 0 Reorder the terms: -72 + 13x + 11x2 = 0 Solving -72 + 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'. -6.545454545 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '6.545454545' to each side of the equation. -6.545454545 + 1.181818182x + 6.545454545 + x2 = 0 + 6.545454545 Reorder the terms: -6.545454545 + 6.545454545 + 1.181818182x + x2 = 0 + 6.545454545 Combine like terms: -6.545454545 + 6.545454545 = 0.000000000 0.000000000 + 1.181818182x + x2 = 0 + 6.545454545 1.181818182x + x2 = 0 + 6.545454545 Combine like terms: 0 + 6.545454545 = 6.545454545 1.181818182x + x2 = 6.545454545 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 = 6.545454545 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 6.545454545 + 0.3491735538 Combine like terms: 6.545454545 + 0.3491735538 = 6.8946280988 0.3491735538 + 1.181818182x + x2 = 6.8946280988 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 6.8946280988 Calculate the square root of the right side: 2.625762384 Break this problem into two subproblems by setting (x + 0.590909091) equal to 2.625762384 and -2.625762384.Subproblem 1
x + 0.590909091 = 2.625762384 Simplifying x + 0.590909091 = 2.625762384 Reorder the terms: 0.590909091 + x = 2.625762384 Solving 0.590909091 + x = 2.625762384 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 = 2.625762384 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 2.625762384 + -0.590909091 x = 2.625762384 + -0.590909091 Combine like terms: 2.625762384 + -0.590909091 = 2.034853293 x = 2.034853293 Simplifying x = 2.034853293Subproblem 2
x + 0.590909091 = -2.625762384 Simplifying x + 0.590909091 = -2.625762384 Reorder the terms: 0.590909091 + x = -2.625762384 Solving 0.590909091 + x = -2.625762384 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 = -2.625762384 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -2.625762384 + -0.590909091 x = -2.625762384 + -0.590909091 Combine like terms: -2.625762384 + -0.590909091 = -3.216671475 x = -3.216671475 Simplifying x = -3.216671475Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.034853293, -3.216671475}
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