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Simplifying 7x2 + 66x + -10 = 0 Reorder the terms: -10 + 66x + 7x2 = 0 Solving -10 + 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'. -1.428571429 + 9.428571429x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 9.428571429x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 9.428571429x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 9.428571429x + x2 = 0 + 1.428571429 9.428571429x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 9.428571429x + x2 = 1.428571429 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 = 1.428571429 + 22.22448980 Reorder the terms: 22.22448980 + 9.428571429x + x2 = 1.428571429 + 22.22448980 Combine like terms: 1.428571429 + 22.22448980 = 23.653061229 22.22448980 + 9.428571429x + x2 = 23.653061229 Factor a perfect square on the left side: (x + 4.714285715)(x + 4.714285715) = 23.653061229 Calculate the square root of the right side: 4.863441295 Break this problem into two subproblems by setting (x + 4.714285715) equal to 4.863441295 and -4.863441295.Subproblem 1
x + 4.714285715 = 4.863441295 Simplifying x + 4.714285715 = 4.863441295 Reorder the terms: 4.714285715 + x = 4.863441295 Solving 4.714285715 + x = 4.863441295 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 = 4.863441295 + -4.714285715 Combine like terms: 4.714285715 + -4.714285715 = 0.000000000 0.000000000 + x = 4.863441295 + -4.714285715 x = 4.863441295 + -4.714285715 Combine like terms: 4.863441295 + -4.714285715 = 0.14915558 x = 0.14915558 Simplifying x = 0.14915558Subproblem 2
x + 4.714285715 = -4.863441295 Simplifying x + 4.714285715 = -4.863441295 Reorder the terms: 4.714285715 + x = -4.863441295 Solving 4.714285715 + x = -4.863441295 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 = -4.863441295 + -4.714285715 Combine like terms: 4.714285715 + -4.714285715 = 0.000000000 0.000000000 + x = -4.863441295 + -4.714285715 x = -4.863441295 + -4.714285715 Combine like terms: -4.863441295 + -4.714285715 = -9.57772701 x = -9.57772701 Simplifying x = -9.57772701Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14915558, -9.57772701}
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