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Simplifying 18x2 + -22x + -24 = 0 Reorder the terms: -24 + -22x + 18x2 = 0 Solving -24 + -22x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -11x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -11x + 9x2)' equal to zero and attempt to solve: Simplifying -12 + -11x + 9x2 = 0 Solving -12 + -11x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -1.222222222x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.222222222x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.222222222x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.222222222x + x2 = 0 + 1.333333333 -1.222222222x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.222222222x + x2 = 1.333333333 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 = 1.333333333 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x + x2 = 1.333333333 + 0.3734567900 Combine like terms: 1.333333333 + 0.3734567900 = 1.706790123 0.3734567900 + -1.222222222x + x2 = 1.706790123 Factor a perfect square on the left side: (x + -0.611111111)(x + -0.611111111) = 1.706790123 Calculate the square root of the right side: 1.306441779 Break this problem into two subproblems by setting (x + -0.611111111) equal to 1.306441779 and -1.306441779.Subproblem 1
x + -0.611111111 = 1.306441779 Simplifying x + -0.611111111 = 1.306441779 Reorder the terms: -0.611111111 + x = 1.306441779 Solving -0.611111111 + x = 1.306441779 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 = 1.306441779 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = 1.306441779 + 0.611111111 x = 1.306441779 + 0.611111111 Combine like terms: 1.306441779 + 0.611111111 = 1.91755289 x = 1.91755289 Simplifying x = 1.91755289Subproblem 2
x + -0.611111111 = -1.306441779 Simplifying x + -0.611111111 = -1.306441779 Reorder the terms: -0.611111111 + x = -1.306441779 Solving -0.611111111 + x = -1.306441779 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 = -1.306441779 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = -1.306441779 + 0.611111111 x = -1.306441779 + 0.611111111 Combine like terms: -1.306441779 + 0.611111111 = -0.695330668 x = -0.695330668 Simplifying x = -0.695330668Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.91755289, -0.695330668}Solution
x = {1.91755289, -0.695330668}
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