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Simplifying 12x + 4 = 9x2 Reorder the terms: 4 + 12x = 9x2 Solving 4 + 12x = 9x2 Solving for variable 'x'. Combine like terms: 9x2 + -9x2 = 0 4 + 12x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.4444444444 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.333333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.4444444444 -1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.333333333x + x2 = 0.4444444444 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 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + -1.333333333x + x2 = 0.8888888886 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.942809041 and -0.942809041.Subproblem 1
x + -0.6666666665 = 0.942809041 Simplifying x + -0.6666666665 = 0.942809041 Reorder the terms: -0.6666666665 + x = 0.942809041 Solving -0.6666666665 + x = 0.942809041 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 = 0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.942809041 + 0.6666666665 x = 0.942809041 + 0.6666666665 Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075 x = 1.6094757075 Simplifying x = 1.6094757075Subproblem 2
x + -0.6666666665 = -0.942809041 Simplifying x + -0.6666666665 = -0.942809041 Reorder the terms: -0.6666666665 + x = -0.942809041 Solving -0.6666666665 + x = -0.942809041 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 = -0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.942809041 + 0.6666666665 x = -0.942809041 + 0.6666666665 Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745 x = -0.2761423745 Simplifying x = -0.2761423745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6094757075, -0.2761423745}
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