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Simplifying 9x2 + -11x + -28 = 0 Reorder the terms: -28 + -11x + 9x2 = 0 Solving -28 + -11x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + -1.222222222x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -1.222222222x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -1.222222222x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -1.222222222x + x2 = 0 + 3.111111111 -1.222222222x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -1.222222222x + x2 = 3.111111111 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 = 3.111111111 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x + x2 = 3.111111111 + 0.3734567900 Combine like terms: 3.111111111 + 0.3734567900 = 3.484567901 0.3734567900 + -1.222222222x + x2 = 3.484567901 Factor a perfect square on the left side: (x + -0.611111111)(x + -0.611111111) = 3.484567901 Calculate the square root of the right side: 1.866699735 Break this problem into two subproblems by setting (x + -0.611111111) equal to 1.866699735 and -1.866699735.Subproblem 1
x + -0.611111111 = 1.866699735 Simplifying x + -0.611111111 = 1.866699735 Reorder the terms: -0.611111111 + x = 1.866699735 Solving -0.611111111 + x = 1.866699735 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 = 1.866699735 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = 1.866699735 + 0.611111111 x = 1.866699735 + 0.611111111 Combine like terms: 1.866699735 + 0.611111111 = 2.477810846 x = 2.477810846 Simplifying x = 2.477810846Subproblem 2
x + -0.611111111 = -1.866699735 Simplifying x + -0.611111111 = -1.866699735 Reorder the terms: -0.611111111 + x = -1.866699735 Solving -0.611111111 + x = -1.866699735 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 = -1.866699735 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = -1.866699735 + 0.611111111 x = -1.866699735 + 0.611111111 Combine like terms: -1.866699735 + 0.611111111 = -1.255588624 x = -1.255588624 Simplifying x = -1.255588624Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.477810846, -1.255588624}
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