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Simplifying 9x2 + 8x + -24 = 0 Reorder the terms: -24 + 8x + 9x2 = 0 Solving -24 + 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'. -2.666666667 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 0.8888888889x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 0.8888888889x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 0.8888888889x + x2 = 0 + 2.666666667 0.8888888889x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 0.8888888889x + x2 = 2.666666667 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 = 2.666666667 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 2.666666667 + 0.1975308642 Combine like terms: 2.666666667 + 0.1975308642 = 2.8641975312 0.1975308642 + 0.8888888889x + x2 = 2.8641975312 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 2.8641975312 Calculate the square root of the right side: 1.692394024 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 1.692394024 and -1.692394024.Subproblem 1
x + 0.4444444445 = 1.692394024 Simplifying x + 0.4444444445 = 1.692394024 Reorder the terms: 0.4444444445 + x = 1.692394024 Solving 0.4444444445 + x = 1.692394024 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 = 1.692394024 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 1.692394024 + -0.4444444445 x = 1.692394024 + -0.4444444445 Combine like terms: 1.692394024 + -0.4444444445 = 1.2479495795 x = 1.2479495795 Simplifying x = 1.2479495795Subproblem 2
x + 0.4444444445 = -1.692394024 Simplifying x + 0.4444444445 = -1.692394024 Reorder the terms: 0.4444444445 + x = -1.692394024 Solving 0.4444444445 + x = -1.692394024 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 = -1.692394024 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -1.692394024 + -0.4444444445 x = -1.692394024 + -0.4444444445 Combine like terms: -1.692394024 + -0.4444444445 = -2.1368384685 x = -2.1368384685 Simplifying x = -2.1368384685Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2479495795, -2.1368384685}
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