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Simplifying 9x2 + -4x + -72 = 0 Reorder the terms: -72 + -4x + 9x2 = 0 Solving -72 + -4x + 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'. -8 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.4444444444x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -0.4444444444x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.4444444444x + x2 = 0 + 8 -0.4444444444x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.4444444444x + x2 = 8 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 8 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 8 + 0.04938271604 Combine like terms: 8 + 0.04938271604 = 8.04938271604 0.04938271604 + -0.4444444444x + x2 = 8.04938271604 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 8.04938271604 Calculate the square root of the right side: 2.837143408 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 2.837143408 and -2.837143408.Subproblem 1
x + -0.2222222222 = 2.837143408 Simplifying x + -0.2222222222 = 2.837143408 Reorder the terms: -0.2222222222 + x = 2.837143408 Solving -0.2222222222 + x = 2.837143408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 2.837143408 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 2.837143408 + 0.2222222222 x = 2.837143408 + 0.2222222222 Combine like terms: 2.837143408 + 0.2222222222 = 3.0593656302 x = 3.0593656302 Simplifying x = 3.0593656302Subproblem 2
x + -0.2222222222 = -2.837143408 Simplifying x + -0.2222222222 = -2.837143408 Reorder the terms: -0.2222222222 + x = -2.837143408 Solving -0.2222222222 + x = -2.837143408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -2.837143408 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -2.837143408 + 0.2222222222 x = -2.837143408 + 0.2222222222 Combine like terms: -2.837143408 + 0.2222222222 = -2.6149211858 x = -2.6149211858 Simplifying x = -2.6149211858Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0593656302, -2.6149211858}
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