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Simplifying 9x2 + -8x + -72 = 0 Reorder the terms: -72 + -8x + 9x2 = 0 Solving -72 + -8x + 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 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.8888888889x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -0.8888888889x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.8888888889x + x2 = 0 + 8 -0.8888888889x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.8888888889x + x2 = 8 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 8 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 8 + 0.1975308642 Combine like terms: 8 + 0.1975308642 = 8.1975308642 0.1975308642 + -0.8888888889x + x2 = 8.1975308642 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 8.1975308642 Calculate the square root of the right side: 2.86313305 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 2.86313305 and -2.86313305.Subproblem 1
x + -0.4444444445 = 2.86313305 Simplifying x + -0.4444444445 = 2.86313305 Reorder the terms: -0.4444444445 + x = 2.86313305 Solving -0.4444444445 + x = 2.86313305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 2.86313305 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 2.86313305 + 0.4444444445 x = 2.86313305 + 0.4444444445 Combine like terms: 2.86313305 + 0.4444444445 = 3.3075774945 x = 3.3075774945 Simplifying x = 3.3075774945Subproblem 2
x + -0.4444444445 = -2.86313305 Simplifying x + -0.4444444445 = -2.86313305 Reorder the terms: -0.4444444445 + x = -2.86313305 Solving -0.4444444445 + x = -2.86313305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -2.86313305 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -2.86313305 + 0.4444444445 x = -2.86313305 + 0.4444444445 Combine like terms: -2.86313305 + 0.4444444445 = -2.4186886055 x = -2.4186886055 Simplifying x = -2.4186886055Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3075774945, -2.4186886055}
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