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Simplifying 60x2 + -77x + -12 = 0 Reorder the terms: -12 + -77x + 60x2 = 0 Solving -12 + -77x + 60x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.2 + -1.283333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.283333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.283333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.283333333x + x2 = 0 + 0.2 -1.283333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.283333333x + x2 = 0.2 The x term is -1.283333333x. Take half its coefficient (-0.6416666665). Square it (0.4117361109) and add it to both sides. Add '0.4117361109' to each side of the equation. -1.283333333x + 0.4117361109 + x2 = 0.2 + 0.4117361109 Reorder the terms: 0.4117361109 + -1.283333333x + x2 = 0.2 + 0.4117361109 Combine like terms: 0.2 + 0.4117361109 = 0.6117361109 0.4117361109 + -1.283333333x + x2 = 0.6117361109 Factor a perfect square on the left side: (x + -0.6416666665)(x + -0.6416666665) = 0.6117361109 Calculate the square root of the right side: 0.782135609 Break this problem into two subproblems by setting (x + -0.6416666665) equal to 0.782135609 and -0.782135609.Subproblem 1
x + -0.6416666665 = 0.782135609 Simplifying x + -0.6416666665 = 0.782135609 Reorder the terms: -0.6416666665 + x = 0.782135609 Solving -0.6416666665 + x = 0.782135609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6416666665' to each side of the equation. -0.6416666665 + 0.6416666665 + x = 0.782135609 + 0.6416666665 Combine like terms: -0.6416666665 + 0.6416666665 = 0.0000000000 0.0000000000 + x = 0.782135609 + 0.6416666665 x = 0.782135609 + 0.6416666665 Combine like terms: 0.782135609 + 0.6416666665 = 1.4238022755 x = 1.4238022755 Simplifying x = 1.4238022755Subproblem 2
x + -0.6416666665 = -0.782135609 Simplifying x + -0.6416666665 = -0.782135609 Reorder the terms: -0.6416666665 + x = -0.782135609 Solving -0.6416666665 + x = -0.782135609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6416666665' to each side of the equation. -0.6416666665 + 0.6416666665 + x = -0.782135609 + 0.6416666665 Combine like terms: -0.6416666665 + 0.6416666665 = 0.0000000000 0.0000000000 + x = -0.782135609 + 0.6416666665 x = -0.782135609 + 0.6416666665 Combine like terms: -0.782135609 + 0.6416666665 = -0.1404689425 x = -0.1404689425 Simplifying x = -0.1404689425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4238022755, -0.1404689425}
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