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Simplifying 18x2 + 22x + -3 = 0 Reorder the terms: -3 + 22x + 18x2 = 0 Solving -3 + 22x + 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'. -0.1666666667 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 1.222222222x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 1.222222222x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0 + 0.1666666667 1.222222222x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 1.222222222x + x2 = 0.1666666667 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = 0.1666666667 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 0.1666666667 + 0.3734567900 Combine like terms: 0.1666666667 + 0.3734567900 = 0.5401234567 0.3734567900 + 1.222222222x + x2 = 0.5401234567 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.5401234567 Calculate the square root of the right side: 0.73493092 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.73493092 and -0.73493092.Subproblem 1
x + 0.611111111 = 0.73493092 Simplifying x + 0.611111111 = 0.73493092 Reorder the terms: 0.611111111 + x = 0.73493092 Solving 0.611111111 + x = 0.73493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 0.73493092 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.73493092 + -0.611111111 x = 0.73493092 + -0.611111111 Combine like terms: 0.73493092 + -0.611111111 = 0.123819809 x = 0.123819809 Simplifying x = 0.123819809Subproblem 2
x + 0.611111111 = -0.73493092 Simplifying x + 0.611111111 = -0.73493092 Reorder the terms: 0.611111111 + x = -0.73493092 Solving 0.611111111 + x = -0.73493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -0.73493092 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.73493092 + -0.611111111 x = -0.73493092 + -0.611111111 Combine like terms: -0.73493092 + -0.611111111 = -1.346042031 x = -1.346042031 Simplifying x = -1.346042031Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.123819809, -1.346042031}
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