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Simplifying 9(x2) + -8(x) + -48 = 0 Reorder the terms: -48 + -8x + 9x2 = 0 Solving -48 + -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'. -5.333333333 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -0.8888888889x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -0.8888888889x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -0.8888888889x + x2 = 0 + 5.333333333 -0.8888888889x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -0.8888888889x + x2 = 5.333333333 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 = 5.333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 5.333333333 + 0.1975308642 Combine like terms: 5.333333333 + 0.1975308642 = 5.5308641972 0.1975308642 + -0.8888888889x + x2 = 5.5308641972 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 5.5308641972 Calculate the square root of the right side: 2.351778943 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 2.351778943 and -2.351778943.Subproblem 1
x + -0.4444444445 = 2.351778943 Simplifying x + -0.4444444445 = 2.351778943 Reorder the terms: -0.4444444445 + x = 2.351778943 Solving -0.4444444445 + x = 2.351778943 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 = 2.351778943 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 2.351778943 + 0.4444444445 x = 2.351778943 + 0.4444444445 Combine like terms: 2.351778943 + 0.4444444445 = 2.7962233875 x = 2.7962233875 Simplifying x = 2.7962233875Subproblem 2
x + -0.4444444445 = -2.351778943 Simplifying x + -0.4444444445 = -2.351778943 Reorder the terms: -0.4444444445 + x = -2.351778943 Solving -0.4444444445 + x = -2.351778943 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 = -2.351778943 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -2.351778943 + 0.4444444445 x = -2.351778943 + 0.4444444445 Combine like terms: -2.351778943 + 0.4444444445 = -1.9073344985 x = -1.9073344985 Simplifying x = -1.9073344985Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7962233875, -1.9073344985}
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