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Simplifying 66x2 + 55x + 9 = 0 Reorder the terms: 9 + 55x + 66x2 = 0 Solving 9 + 55x + 66x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 66 the coefficient of the squared term: Divide each side by '66'. 0.1363636364 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.1363636364' to each side of the equation. 0.1363636364 + 0.8333333333x + -0.1363636364 + x2 = 0 + -0.1363636364 Reorder the terms: 0.1363636364 + -0.1363636364 + 0.8333333333x + x2 = 0 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + 0.8333333333x + x2 = 0 + -0.1363636364 0.8333333333x + x2 = 0 + -0.1363636364 Combine like terms: 0 + -0.1363636364 = -0.1363636364 0.8333333333x + x2 = -0.1363636364 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = -0.1363636364 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -0.1363636364 + 0.1736111111 Combine like terms: -0.1363636364 + 0.1736111111 = 0.0372474747 0.1736111111 + 0.8333333333x + x2 = 0.0372474747 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 0.0372474747 Calculate the square root of the right side: 0.192996048 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 0.192996048 and -0.192996048.Subproblem 1
x + 0.4166666667 = 0.192996048 Simplifying x + 0.4166666667 = 0.192996048 Reorder the terms: 0.4166666667 + x = 0.192996048 Solving 0.4166666667 + x = 0.192996048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.192996048 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.192996048 + -0.4166666667 x = 0.192996048 + -0.4166666667 Combine like terms: 0.192996048 + -0.4166666667 = -0.2236706187 x = -0.2236706187 Simplifying x = -0.2236706187Subproblem 2
x + 0.4166666667 = -0.192996048 Simplifying x + 0.4166666667 = -0.192996048 Reorder the terms: 0.4166666667 + x = -0.192996048 Solving 0.4166666667 + x = -0.192996048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.192996048 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.192996048 + -0.4166666667 x = -0.192996048 + -0.4166666667 Combine like terms: -0.192996048 + -0.4166666667 = -0.6096627147 x = -0.6096627147 Simplifying x = -0.6096627147Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2236706187, -0.6096627147}
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