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Simplifying 7x2 + -66x + -252 = 0 Reorder the terms: -252 + -66x + 7x2 = 0 Solving -252 + -66x + 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'. -36 + -9.428571429x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -9.428571429x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -9.428571429x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -9.428571429x + x2 = 0 + 36 -9.428571429x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -9.428571429x + x2 = 36 The x term is -9.428571429x. Take half its coefficient (-4.714285715). Square it (22.22448980) and add it to both sides. Add '22.22448980' to each side of the equation. -9.428571429x + 22.22448980 + x2 = 36 + 22.22448980 Reorder the terms: 22.22448980 + -9.428571429x + x2 = 36 + 22.22448980 Combine like terms: 36 + 22.22448980 = 58.2244898 22.22448980 + -9.428571429x + x2 = 58.2244898 Factor a perfect square on the left side: (x + -4.714285715)(x + -4.714285715) = 58.2244898 Calculate the square root of the right side: 7.630497349 Break this problem into two subproblems by setting (x + -4.714285715) equal to 7.630497349 and -7.630497349.Subproblem 1
x + -4.714285715 = 7.630497349 Simplifying x + -4.714285715 = 7.630497349 Reorder the terms: -4.714285715 + x = 7.630497349 Solving -4.714285715 + x = 7.630497349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = 7.630497349 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = 7.630497349 + 4.714285715 x = 7.630497349 + 4.714285715 Combine like terms: 7.630497349 + 4.714285715 = 12.344783064 x = 12.344783064 Simplifying x = 12.344783064Subproblem 2
x + -4.714285715 = -7.630497349 Simplifying x + -4.714285715 = -7.630497349 Reorder the terms: -4.714285715 + x = -7.630497349 Solving -4.714285715 + x = -7.630497349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = -7.630497349 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = -7.630497349 + 4.714285715 x = -7.630497349 + 4.714285715 Combine like terms: -7.630497349 + 4.714285715 = -2.916211634 x = -2.916211634 Simplifying x = -2.916211634Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.344783064, -2.916211634}
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