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Simplifying 18x2 + 61x + 7 = 0 Reorder the terms: 7 + 61x + 18x2 = 0 Solving 7 + 61x + 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 + 3.388888889x + x2 = 0 Move the constant term to the right: Add '-0.3888888889' to each side of the equation. 0.3888888889 + 3.388888889x + -0.3888888889 + x2 = 0 + -0.3888888889 Reorder the terms: 0.3888888889 + -0.3888888889 + 3.388888889x + x2 = 0 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + 3.388888889x + x2 = 0 + -0.3888888889 3.388888889x + x2 = 0 + -0.3888888889 Combine like terms: 0 + -0.3888888889 = -0.3888888889 3.388888889x + x2 = -0.3888888889 The x term is 3.388888889x. Take half its coefficient (1.694444445). Square it (2.871141977) and add it to both sides. Add '2.871141977' to each side of the equation. 3.388888889x + 2.871141977 + x2 = -0.3888888889 + 2.871141977 Reorder the terms: 2.871141977 + 3.388888889x + x2 = -0.3888888889 + 2.871141977 Combine like terms: -0.3888888889 + 2.871141977 = 2.4822530881 2.871141977 + 3.388888889x + x2 = 2.4822530881 Factor a perfect square on the left side: (x + 1.694444445)(x + 1.694444445) = 2.4822530881 Calculate the square root of the right side: 1.575516769 Break this problem into two subproblems by setting (x + 1.694444445) equal to 1.575516769 and -1.575516769.Subproblem 1
x + 1.694444445 = 1.575516769 Simplifying x + 1.694444445 = 1.575516769 Reorder the terms: 1.694444445 + x = 1.575516769 Solving 1.694444445 + x = 1.575516769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.694444445' to each side of the equation. 1.694444445 + -1.694444445 + x = 1.575516769 + -1.694444445 Combine like terms: 1.694444445 + -1.694444445 = 0.000000000 0.000000000 + x = 1.575516769 + -1.694444445 x = 1.575516769 + -1.694444445 Combine like terms: 1.575516769 + -1.694444445 = -0.118927676 x = -0.118927676 Simplifying x = -0.118927676Subproblem 2
x + 1.694444445 = -1.575516769 Simplifying x + 1.694444445 = -1.575516769 Reorder the terms: 1.694444445 + x = -1.575516769 Solving 1.694444445 + x = -1.575516769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.694444445' to each side of the equation. 1.694444445 + -1.694444445 + x = -1.575516769 + -1.694444445 Combine like terms: 1.694444445 + -1.694444445 = 0.000000000 0.000000000 + x = -1.575516769 + -1.694444445 x = -1.575516769 + -1.694444445 Combine like terms: -1.575516769 + -1.694444445 = -3.269961214 x = -3.269961214 Simplifying x = -3.269961214Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.118927676, -3.269961214}
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