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Simplifying 9x2 + -12x = 1 Reorder the terms: -12x + 9x2 = 1 Solving -12x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -12x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -1.333333333x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -1.333333333x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.1111111111 -1.333333333x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -1.333333333x + x2 = 0.1111111111 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 = 0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.1111111111 + 0.4444444442 Combine like terms: 0.1111111111 + 0.4444444442 = 0.5555555553 0.4444444442 + -1.333333333x + x2 = 0.5555555553 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.5555555553 Calculate the square root of the right side: 0.745355992 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.745355992 and -0.745355992.Subproblem 1
x + -0.6666666665 = 0.745355992 Simplifying x + -0.6666666665 = 0.745355992 Reorder the terms: -0.6666666665 + x = 0.745355992 Solving -0.6666666665 + x = 0.745355992 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 = 0.745355992 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.745355992 + 0.6666666665 x = 0.745355992 + 0.6666666665 Combine like terms: 0.745355992 + 0.6666666665 = 1.4120226585 x = 1.4120226585 Simplifying x = 1.4120226585Subproblem 2
x + -0.6666666665 = -0.745355992 Simplifying x + -0.6666666665 = -0.745355992 Reorder the terms: -0.6666666665 + x = -0.745355992 Solving -0.6666666665 + x = -0.745355992 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 = -0.745355992 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.745355992 + 0.6666666665 x = -0.745355992 + 0.6666666665 Combine like terms: -0.745355992 + 0.6666666665 = -0.0786893255 x = -0.0786893255 Simplifying x = -0.0786893255Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4120226585, -0.0786893255}
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