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Simplifying -18x2 + 65x + 7 = 0 Reorder the terms: 7 + 65x + -18x2 = 0 Solving 7 + 65x + -18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.3888888889 + -3.611111111x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -3.611111111x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -3.611111111x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -3.611111111x + x2 = 0 + 0.3888888889 -3.611111111x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -3.611111111x + x2 = 0.3888888889 The x term is -3.611111111x. Take half its coefficient (-1.805555556). Square it (3.260030866) and add it to both sides. Add '3.260030866' to each side of the equation. -3.611111111x + 3.260030866 + x2 = 0.3888888889 + 3.260030866 Reorder the terms: 3.260030866 + -3.611111111x + x2 = 0.3888888889 + 3.260030866 Combine like terms: 0.3888888889 + 3.260030866 = 3.6489197549 3.260030866 + -3.611111111x + x2 = 3.6489197549 Factor a perfect square on the left side: (x + -1.805555556)(x + -1.805555556) = 3.6489197549 Calculate the square root of the right side: 1.910214583 Break this problem into two subproblems by setting (x + -1.805555556) equal to 1.910214583 and -1.910214583.Subproblem 1
x + -1.805555556 = 1.910214583 Simplifying x + -1.805555556 = 1.910214583 Reorder the terms: -1.805555556 + x = 1.910214583 Solving -1.805555556 + x = 1.910214583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.805555556' to each side of the equation. -1.805555556 + 1.805555556 + x = 1.910214583 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + x = 1.910214583 + 1.805555556 x = 1.910214583 + 1.805555556 Combine like terms: 1.910214583 + 1.805555556 = 3.715770139 x = 3.715770139 Simplifying x = 3.715770139Subproblem 2
x + -1.805555556 = -1.910214583 Simplifying x + -1.805555556 = -1.910214583 Reorder the terms: -1.805555556 + x = -1.910214583 Solving -1.805555556 + x = -1.910214583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.805555556' to each side of the equation. -1.805555556 + 1.805555556 + x = -1.910214583 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + x = -1.910214583 + 1.805555556 x = -1.910214583 + 1.805555556 Combine like terms: -1.910214583 + 1.805555556 = -0.104659027 x = -0.104659027 Simplifying x = -0.104659027Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.715770139, -0.104659027}
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