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Simplifying 0 = 6x2 + -10x + 19 Reorder the terms: 0 = 19 + -10x + 6x2 Solving 0 = 19 + -10x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -19 = -19 -19 + 10x + -6x2 = 19 + -10x + 6x2 + -19 + 10x + -6x2 Reorder the terms: -19 + 10x + -6x2 = 19 + -19 + -10x + 10x + 6x2 + -6x2 Combine like terms: 19 + -19 = 0 -19 + 10x + -6x2 = 0 + -10x + 10x + 6x2 + -6x2 -19 + 10x + -6x2 = -10x + 10x + 6x2 + -6x2 Combine like terms: -10x + 10x = 0 -19 + 10x + -6x2 = 0 + 6x2 + -6x2 -19 + 10x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -19 + 10x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 3.166666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-3.166666667' to each side of the equation. 3.166666667 + -1.666666667x + -3.166666667 + x2 = 0 + -3.166666667 Reorder the terms: 3.166666667 + -3.166666667 + -1.666666667x + x2 = 0 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -3.166666667 -1.666666667x + x2 = 0 + -3.166666667 Combine like terms: 0 + -3.166666667 = -3.166666667 -1.666666667x + x2 = -3.166666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -3.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -3.166666667 + 0.6944444447 Combine like terms: -3.166666667 + 0.6944444447 = -2.4722222223 0.6944444447 + -1.666666667x + x2 = -2.4722222223 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -2.4722222223 Can't calculate square root of the right side. The solution to this equation could not be determined.
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