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Simplifying 0 = 3x2 + -10x + 32 Reorder the terms: 0 = 32 + -10x + 3x2 Solving 0 = 32 + -10x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + 10x + -3x2 = 32 + -10x + 3x2 + -32 + 10x + -3x2 Reorder the terms: -32 + 10x + -3x2 = 32 + -32 + -10x + 10x + 3x2 + -3x2 Combine like terms: 32 + -32 = 0 -32 + 10x + -3x2 = 0 + -10x + 10x + 3x2 + -3x2 -32 + 10x + -3x2 = -10x + 10x + 3x2 + -3x2 Combine like terms: -10x + 10x = 0 -32 + 10x + -3x2 = 0 + 3x2 + -3x2 -32 + 10x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -32 + 10x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10.66666667 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + -3.333333333x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + -3.333333333x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + -3.333333333x + x2 = 0 + -10.66666667 -3.333333333x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 -3.333333333x + x2 = -10.66666667 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -10.66666667 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -10.66666667 + 2.777777779 Combine like terms: -10.66666667 + 2.777777779 = -7.888888891 2.777777779 + -3.333333333x + x2 = -7.888888891 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = -7.888888891 Can't calculate square root of the right side. The solution to this equation could not be determined.
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