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Simplifying (7x2 + -5x + 3) + -1(5x2 + -4) = 0 Reorder the terms: (3 + -5x + 7x2) + -1(5x2 + -4) = 0 Remove parenthesis around (3 + -5x + 7x2) 3 + -5x + 7x2 + -1(5x2 + -4) = 0 Reorder the terms: 3 + -5x + 7x2 + -1(-4 + 5x2) = 0 3 + -5x + 7x2 + (-4 * -1 + 5x2 * -1) = 0 3 + -5x + 7x2 + (4 + -5x2) = 0 Reorder the terms: 3 + 4 + -5x + 7x2 + -5x2 = 0 Combine like terms: 3 + 4 = 7 7 + -5x + 7x2 + -5x2 = 0 Combine like terms: 7x2 + -5x2 = 2x2 7 + -5x + 2x2 = 0 Solving 7 + -5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -2.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -2.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -2.5x + x2 = 0 + -3.5 -2.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -2.5x + x2 = -3.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -3.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -3.5 + 1.5625 Combine like terms: -3.5 + 1.5625 = -1.9375 1.5625 + -2.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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