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Simplifying 31.563 = -16t2 + 10t + 30 Reorder the terms: 31.563 = 30 + 10t + -16t2 Solving 31.563 = 30 + 10t + -16t2 Solving for variable 't'. Combine like terms: 31.563 + -30 = 1.563 1.563 + -10t + 16t2 = 30 + 10t + -16t2 + -30 + -10t + 16t2 Reorder the terms: 1.563 + -10t + 16t2 = 30 + -30 + 10t + -10t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 1.563 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 1.563 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 1.563 + -10t + 16t2 = 0 + -16t2 + 16t2 1.563 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1.563 + -10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0976875 + -0.625t + t2 = 0 Move the constant term to the right: Add '-0.0976875' to each side of the equation. 0.0976875 + -0.625t + -0.0976875 + t2 = 0 + -0.0976875 Reorder the terms: 0.0976875 + -0.0976875 + -0.625t + t2 = 0 + -0.0976875 Combine like terms: 0.0976875 + -0.0976875 = 0.0000000 0.0000000 + -0.625t + t2 = 0 + -0.0976875 -0.625t + t2 = 0 + -0.0976875 Combine like terms: 0 + -0.0976875 = -0.0976875 -0.625t + t2 = -0.0976875 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = -0.0976875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = -0.0976875 + 0.09765625 Combine like terms: -0.0976875 + 0.09765625 = -0.00003125 0.09765625 + -0.625t + t2 = -0.00003125 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = -0.00003125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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