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Simplifying 0 = -16t2 + 975t + 5 Reorder the terms: 0 = 5 + 975t + -16t2 Solving 0 = 5 + 975t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -975t + 16t2 = 5 + 975t + -16t2 + -5 + -975t + 16t2 Reorder the terms: -5 + -975t + 16t2 = 5 + -5 + 975t + -975t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -975t + 16t2 = 0 + 975t + -975t + -16t2 + 16t2 -5 + -975t + 16t2 = 975t + -975t + -16t2 + 16t2 Combine like terms: 975t + -975t = 0 -5 + -975t + 16t2 = 0 + -16t2 + 16t2 -5 + -975t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -975t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -60.9375t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -60.9375t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -60.9375t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -60.9375t + t2 = 0 + 0.3125 -60.9375t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -60.9375t + t2 = 0.3125 The t term is -60.9375t. Take half its coefficient (-30.46875). Square it (928.3447266) and add it to both sides. Add '928.3447266' to each side of the equation. -60.9375t + 928.3447266 + t2 = 0.3125 + 928.3447266 Reorder the terms: 928.3447266 + -60.9375t + t2 = 0.3125 + 928.3447266 Combine like terms: 0.3125 + 928.3447266 = 928.6572266 928.3447266 + -60.9375t + t2 = 928.6572266 Factor a perfect square on the left side: (t + -30.46875)(t + -30.46875) = 928.6572266 Calculate the square root of the right side: 30.473877774 Break this problem into two subproblems by setting (t + -30.46875) equal to 30.473877774 and -30.473877774.Subproblem 1
t + -30.46875 = 30.473877774 Simplifying t + -30.46875 = 30.473877774 Reorder the terms: -30.46875 + t = 30.473877774 Solving -30.46875 + t = 30.473877774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30.46875' to each side of the equation. -30.46875 + 30.46875 + t = 30.473877774 + 30.46875 Combine like terms: -30.46875 + 30.46875 = 0.00000 0.00000 + t = 30.473877774 + 30.46875 t = 30.473877774 + 30.46875 Combine like terms: 30.473877774 + 30.46875 = 60.942627774 t = 60.942627774 Simplifying t = 60.942627774Subproblem 2
t + -30.46875 = -30.473877774 Simplifying t + -30.46875 = -30.473877774 Reorder the terms: -30.46875 + t = -30.473877774 Solving -30.46875 + t = -30.473877774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30.46875' to each side of the equation. -30.46875 + 30.46875 + t = -30.473877774 + 30.46875 Combine like terms: -30.46875 + 30.46875 = 0.00000 0.00000 + t = -30.473877774 + 30.46875 t = -30.473877774 + 30.46875 Combine like terms: -30.473877774 + 30.46875 = -0.005127774 t = -0.005127774 Simplifying t = -0.005127774Solution
The solution to the problem is based on the solutions from the subproblems. t = {60.942627774, -0.005127774}
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