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Simplifying 443 = 16t2 + -4t + 470 Reorder the terms: 443 = 470 + -4t + 16t2 Solving 443 = 470 + -4t + 16t2 Solving for variable 't'. Combine like terms: 443 + -470 = -27 -27 + 4t + -16t2 = 470 + -4t + 16t2 + -470 + 4t + -16t2 Reorder the terms: -27 + 4t + -16t2 = 470 + -470 + -4t + 4t + 16t2 + -16t2 Combine like terms: 470 + -470 = 0 -27 + 4t + -16t2 = 0 + -4t + 4t + 16t2 + -16t2 -27 + 4t + -16t2 = -4t + 4t + 16t2 + -16t2 Combine like terms: -4t + 4t = 0 -27 + 4t + -16t2 = 0 + 16t2 + -16t2 -27 + 4t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -27 + 4t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.6875 + -0.25t + t2 = 0 Move the constant term to the right: Add '-1.6875' to each side of the equation. 1.6875 + -0.25t + -1.6875 + t2 = 0 + -1.6875 Reorder the terms: 1.6875 + -1.6875 + -0.25t + t2 = 0 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + -0.25t + t2 = 0 + -1.6875 -0.25t + t2 = 0 + -1.6875 Combine like terms: 0 + -1.6875 = -1.6875 -0.25t + t2 = -1.6875 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = -1.6875 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -1.6875 + 0.015625 Combine like terms: -1.6875 + 0.015625 = -1.671875 0.015625 + -0.25t + t2 = -1.671875 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -1.671875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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