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Simplifying 0.75x2 + -1x + -2.67 = 0 Reorder the terms: -2.67 + -1x + 0.75x2 = 0 Solving -2.67 + -1x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. -3.56 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '3.56' to each side of the equation. -3.56 + -1.333333333x + 3.56 + x2 = 0 + 3.56 Reorder the terms: -3.56 + 3.56 + -1.333333333x + x2 = 0 + 3.56 Combine like terms: -3.56 + 3.56 = 0.00 0.00 + -1.333333333x + x2 = 0 + 3.56 -1.333333333x + x2 = 0 + 3.56 Combine like terms: 0 + 3.56 = 3.56 -1.333333333x + x2 = 3.56 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 = 3.56 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 3.56 + 0.4444444442 Combine like terms: 3.56 + 0.4444444442 = 4.0044444442 0.4444444442 + -1.333333333x + x2 = 4.0044444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 4.0044444442 Calculate the square root of the right side: 2.001110803 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.001110803 and -2.001110803.Subproblem 1
x + -0.6666666665 = 2.001110803 Simplifying x + -0.6666666665 = 2.001110803 Reorder the terms: -0.6666666665 + x = 2.001110803 Solving -0.6666666665 + x = 2.001110803 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 = 2.001110803 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.001110803 + 0.6666666665 x = 2.001110803 + 0.6666666665 Combine like terms: 2.001110803 + 0.6666666665 = 2.6677774695 x = 2.6677774695 Simplifying x = 2.6677774695Subproblem 2
x + -0.6666666665 = -2.001110803 Simplifying x + -0.6666666665 = -2.001110803 Reorder the terms: -0.6666666665 + x = -2.001110803 Solving -0.6666666665 + x = -2.001110803 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 = -2.001110803 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.001110803 + 0.6666666665 x = -2.001110803 + 0.6666666665 Combine like terms: -2.001110803 + 0.6666666665 = -1.3344441365 x = -1.3344441365 Simplifying x = -1.3344441365Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6677774695, -1.3344441365}
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