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Simplifying 9x2 + -63x + 82 = 0 Reorder the terms: 82 + -63x + 9x2 = 0 Solving 82 + -63x + 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'. 9.111111111 + -7x + x2 = 0 Move the constant term to the right: Add '-9.111111111' to each side of the equation. 9.111111111 + -7x + -9.111111111 + x2 = 0 + -9.111111111 Reorder the terms: 9.111111111 + -9.111111111 + -7x + x2 = 0 + -9.111111111 Combine like terms: 9.111111111 + -9.111111111 = 0.000000000 0.000000000 + -7x + x2 = 0 + -9.111111111 -7x + x2 = 0 + -9.111111111 Combine like terms: 0 + -9.111111111 = -9.111111111 -7x + x2 = -9.111111111 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -9.111111111 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -9.111111111 + 12.25 Combine like terms: -9.111111111 + 12.25 = 3.138888889 12.25 + -7x + x2 = 3.138888889 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 3.138888889 Calculate the square root of the right side: 1.771690969 Break this problem into two subproblems by setting (x + -3.5) equal to 1.771690969 and -1.771690969.Subproblem 1
x + -3.5 = 1.771690969 Simplifying x + -3.5 = 1.771690969 Reorder the terms: -3.5 + x = 1.771690969 Solving -3.5 + x = 1.771690969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.771690969 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.771690969 + 3.5 x = 1.771690969 + 3.5 Combine like terms: 1.771690969 + 3.5 = 5.271690969 x = 5.271690969 Simplifying x = 5.271690969Subproblem 2
x + -3.5 = -1.771690969 Simplifying x + -3.5 = -1.771690969 Reorder the terms: -3.5 + x = -1.771690969 Solving -3.5 + x = -1.771690969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.771690969 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.771690969 + 3.5 x = -1.771690969 + 3.5 Combine like terms: -1.771690969 + 3.5 = 1.728309031 x = 1.728309031 Simplifying x = 1.728309031Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.271690969, 1.728309031}
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