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Simplifying 9x2 + 12x + -8 = 9 Reorder the terms: -8 + 12x + 9x2 = 9 Solving -8 + 12x + 9x2 = 9 Solving for variable 'x'. Reorder the terms: -8 + -9 + 12x + 9x2 = 9 + -9 Combine like terms: -8 + -9 = -17 -17 + 12x + 9x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -17 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 1.333333333x + 1.888888889 + x2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 1.333333333x + x2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 1.888888889 1.333333333x + x2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 1.333333333x + x2 = 1.888888889 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 1.888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1.888888889 + 0.4444444442 Combine like terms: 1.888888889 + 0.4444444442 = 2.3333333332 0.4444444442 + 1.333333333x + x2 = 2.3333333332 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 2.3333333332 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.527525232 and -1.527525232.Subproblem 1
x + 0.6666666665 = 1.527525232 Simplifying x + 0.6666666665 = 1.527525232 Reorder the terms: 0.6666666665 + x = 1.527525232 Solving 0.6666666665 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.527525232 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.527525232 + -0.6666666665 x = 1.527525232 + -0.6666666665 Combine like terms: 1.527525232 + -0.6666666665 = 0.8608585655 x = 0.8608585655 Simplifying x = 0.8608585655Subproblem 2
x + 0.6666666665 = -1.527525232 Simplifying x + 0.6666666665 = -1.527525232 Reorder the terms: 0.6666666665 + x = -1.527525232 Solving 0.6666666665 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.527525232 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.527525232 + -0.6666666665 x = -1.527525232 + -0.6666666665 Combine like terms: -1.527525232 + -0.6666666665 = -2.1941918985 x = -2.1941918985 Simplifying x = -2.1941918985Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8608585655, -2.1941918985}
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