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Simplifying 7a * 7a + 32 = 7 + -40a Reorder the terms for easier multiplication: 7 * 7a * a + 32 = 7 + -40a Multiply 7 * 7 49a * a + 32 = 7 + -40a Multiply a * a 49a2 + 32 = 7 + -40a Reorder the terms: 32 + 49a2 = 7 + -40a Solving 32 + 49a2 = 7 + -40a Solving for variable 'a'. Reorder the terms: 32 + -7 + 40a + 49a2 = 7 + -40a + -7 + 40a Combine like terms: 32 + -7 = 25 25 + 40a + 49a2 = 7 + -40a + -7 + 40a Reorder the terms: 25 + 40a + 49a2 = 7 + -7 + -40a + 40a Combine like terms: 7 + -7 = 0 25 + 40a + 49a2 = 0 + -40a + 40a 25 + 40a + 49a2 = -40a + 40a Combine like terms: -40a + 40a = 0 25 + 40a + 49a2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.5102040816 + 0.8163265306a + a2 = 0 Move the constant term to the right: Add '-0.5102040816' to each side of the equation. 0.5102040816 + 0.8163265306a + -0.5102040816 + a2 = 0 + -0.5102040816 Reorder the terms: 0.5102040816 + -0.5102040816 + 0.8163265306a + a2 = 0 + -0.5102040816 Combine like terms: 0.5102040816 + -0.5102040816 = 0.0000000000 0.0000000000 + 0.8163265306a + a2 = 0 + -0.5102040816 0.8163265306a + a2 = 0 + -0.5102040816 Combine like terms: 0 + -0.5102040816 = -0.5102040816 0.8163265306a + a2 = -0.5102040816 The a term is 0.8163265306a. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306a + 0.1665972511 + a2 = -0.5102040816 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306a + a2 = -0.5102040816 + 0.1665972511 Combine like terms: -0.5102040816 + 0.1665972511 = -0.3436068305 0.1665972511 + 0.8163265306a + a2 = -0.3436068305 Factor a perfect square on the left side: (a + 0.4081632653)(a + 0.4081632653) = -0.3436068305 Can't calculate square root of the right side. The solution to this equation could not be determined.
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