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Simplifying 22.58 = -16t2 + 15t + 12 Reorder the terms: 22.58 = 12 + 15t + -16t2 Solving 22.58 = 12 + 15t + -16t2 Solving for variable 't'. Combine like terms: 22.58 + -12 = 10.58 10.58 + -15t + 16t2 = 12 + 15t + -16t2 + -12 + -15t + 16t2 Reorder the terms: 10.58 + -15t + 16t2 = 12 + -12 + 15t + -15t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 10.58 + -15t + 16t2 = 0 + 15t + -15t + -16t2 + 16t2 10.58 + -15t + 16t2 = 15t + -15t + -16t2 + 16t2 Combine like terms: 15t + -15t = 0 10.58 + -15t + 16t2 = 0 + -16t2 + 16t2 10.58 + -15t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10.58 + -15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.66125 + -0.9375t + t2 = 0 Move the constant term to the right: Add '-0.66125' to each side of the equation. 0.66125 + -0.9375t + -0.66125 + t2 = 0 + -0.66125 Reorder the terms: 0.66125 + -0.66125 + -0.9375t + t2 = 0 + -0.66125 Combine like terms: 0.66125 + -0.66125 = 0.00000 0.00000 + -0.9375t + t2 = 0 + -0.66125 -0.9375t + t2 = 0 + -0.66125 Combine like terms: 0 + -0.66125 = -0.66125 -0.9375t + t2 = -0.66125 The t term is -0.9375t. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375t + 0.2197265625 + t2 = -0.66125 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = -0.66125 + 0.2197265625 Combine like terms: -0.66125 + 0.2197265625 = -0.4415234375 0.2197265625 + -0.9375t + t2 = -0.4415234375 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = -0.4415234375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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