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Simplifying 9x2 = 8 + -3x Solving 9x2 = 8 + -3x Solving for variable 'x'. Reorder the terms: -8 + 3x + 9x2 = 8 + -3x + -8 + 3x Reorder the terms: -8 + 3x + 9x2 = 8 + -8 + -3x + 3x Combine like terms: 8 + -8 = 0 -8 + 3x + 9x2 = 0 + -3x + 3x -8 + 3x + 9x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -8 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.3333333333x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.3333333333x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.8888888889 0.3333333333x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.3333333333x + x2 = 0.8888888889 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.8888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.8888888889 + 0.02777777779 Combine like terms: 0.8888888889 + 0.02777777779 = 0.91666666669 0.02777777779 + 0.3333333333x + x2 = 0.91666666669 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.91666666669 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.957427108 and -0.957427108.Subproblem 1
x + 0.1666666667 = 0.957427108 Simplifying x + 0.1666666667 = 0.957427108 Reorder the terms: 0.1666666667 + x = 0.957427108 Solving 0.1666666667 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.957427108 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.957427108 + -0.1666666667 x = 0.957427108 + -0.1666666667 Combine like terms: 0.957427108 + -0.1666666667 = 0.7907604413 x = 0.7907604413 Simplifying x = 0.7907604413Subproblem 2
x + 0.1666666667 = -0.957427108 Simplifying x + 0.1666666667 = -0.957427108 Reorder the terms: 0.1666666667 + x = -0.957427108 Solving 0.1666666667 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.957427108 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.957427108 + -0.1666666667 x = -0.957427108 + -0.1666666667 Combine like terms: -0.957427108 + -0.1666666667 = -1.1240937747 x = -1.1240937747 Simplifying x = -1.1240937747Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7907604413, -1.1240937747}
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