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Simplifying (6f2 + -9f + 10) + -1(2f2 + -1f + 3) = 0 Reorder the terms: (10 + -9f + 6f2) + -1(2f2 + -1f + 3) = 0 Remove parenthesis around (10 + -9f + 6f2) 10 + -9f + 6f2 + -1(2f2 + -1f + 3) = 0 Reorder the terms: 10 + -9f + 6f2 + -1(3 + -1f + 2f2) = 0 10 + -9f + 6f2 + (3 * -1 + -1f * -1 + 2f2 * -1) = 0 10 + -9f + 6f2 + (-3 + 1f + -2f2) = 0 Reorder the terms: 10 + -3 + -9f + 1f + 6f2 + -2f2 = 0 Combine like terms: 10 + -3 = 7 7 + -9f + 1f + 6f2 + -2f2 = 0 Combine like terms: -9f + 1f = -8f 7 + -8f + 6f2 + -2f2 = 0 Combine like terms: 6f2 + -2f2 = 4f2 7 + -8f + 4f2 = 0 Solving 7 + -8f + 4f2 = 0 Solving for variable 'f'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -2f + f2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -2f + -1.75 + f2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -2f + f2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -2f + f2 = 0 + -1.75 -2f + f2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -2f + f2 = -1.75 The f term is -2f. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2f + 1 + f2 = -1.75 + 1 Reorder the terms: 1 + -2f + f2 = -1.75 + 1 Combine like terms: -1.75 + 1 = -0.75 1 + -2f + f2 = -0.75 Factor a perfect square on the left side: (f + -1)(f + -1) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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