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Simplifying 11x2 + -78x + -72 = 0 Reorder the terms: -72 + -78x + 11x2 = 0 Solving -72 + -78x + 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 + -7.090909091x + x2 = 0 Move the constant term to the right: Add '6.545454545' to each side of the equation. -6.545454545 + -7.090909091x + 6.545454545 + x2 = 0 + 6.545454545 Reorder the terms: -6.545454545 + 6.545454545 + -7.090909091x + x2 = 0 + 6.545454545 Combine like terms: -6.545454545 + 6.545454545 = 0.000000000 0.000000000 + -7.090909091x + x2 = 0 + 6.545454545 -7.090909091x + x2 = 0 + 6.545454545 Combine like terms: 0 + 6.545454545 = 6.545454545 -7.090909091x + x2 = 6.545454545 The x term is -7.090909091x. Take half its coefficient (-3.545454546). Square it (12.57024794) and add it to both sides. Add '12.57024794' to each side of the equation. -7.090909091x + 12.57024794 + x2 = 6.545454545 + 12.57024794 Reorder the terms: 12.57024794 + -7.090909091x + x2 = 6.545454545 + 12.57024794 Combine like terms: 6.545454545 + 12.57024794 = 19.115702485 12.57024794 + -7.090909091x + x2 = 19.115702485 Factor a perfect square on the left side: (x + -3.545454546)(x + -3.545454546) = 19.115702485 Calculate the square root of the right side: 4.372150785 Break this problem into two subproblems by setting (x + -3.545454546) equal to 4.372150785 and -4.372150785.Subproblem 1
x + -3.545454546 = 4.372150785 Simplifying x + -3.545454546 = 4.372150785 Reorder the terms: -3.545454546 + x = 4.372150785 Solving -3.545454546 + x = 4.372150785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.545454546' to each side of the equation. -3.545454546 + 3.545454546 + x = 4.372150785 + 3.545454546 Combine like terms: -3.545454546 + 3.545454546 = 0.000000000 0.000000000 + x = 4.372150785 + 3.545454546 x = 4.372150785 + 3.545454546 Combine like terms: 4.372150785 + 3.545454546 = 7.917605331 x = 7.917605331 Simplifying x = 7.917605331Subproblem 2
x + -3.545454546 = -4.372150785 Simplifying x + -3.545454546 = -4.372150785 Reorder the terms: -3.545454546 + x = -4.372150785 Solving -3.545454546 + x = -4.372150785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.545454546' to each side of the equation. -3.545454546 + 3.545454546 + x = -4.372150785 + 3.545454546 Combine like terms: -3.545454546 + 3.545454546 = 0.000000000 0.000000000 + x = -4.372150785 + 3.545454546 x = -4.372150785 + 3.545454546 Combine like terms: -4.372150785 + 3.545454546 = -0.826696239 x = -0.826696239 Simplifying x = -0.826696239Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.917605331, -0.826696239}
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