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Simplifying (5t2 + -2t + 7) + (-1t2 + 6t + -4) = 0 Reorder the terms: (7 + -2t + 5t2) + (-1t2 + 6t + -4) = 0 Remove parenthesis around (7 + -2t + 5t2) 7 + -2t + 5t2 + (-1t2 + 6t + -4) = 0 Reorder the terms: 7 + -2t + 5t2 + (-4 + 6t + -1t2) = 0 Remove parenthesis around (-4 + 6t + -1t2) 7 + -2t + 5t2 + -4 + 6t + -1t2 = 0 Reorder the terms: 7 + -4 + -2t + 6t + 5t2 + -1t2 = 0 Combine like terms: 7 + -4 = 3 3 + -2t + 6t + 5t2 + -1t2 = 0 Combine like terms: -2t + 6t = 4t 3 + 4t + 5t2 + -1t2 = 0 Combine like terms: 5t2 + -1t2 = 4t2 3 + 4t + 4t2 = 0 Solving 3 + 4t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t + t2 = 0 + -0.75 t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 t + t2 = -0.75 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = -0.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 1.25 + t2 = -0.5 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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