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Simplifying 313 = -16t2 + 153t + 3 Reorder the terms: 313 = 3 + 153t + -16t2 Solving 313 = 3 + 153t + -16t2 Solving for variable 't'. Combine like terms: 313 + -3 = 310 310 + -153t + 16t2 = 3 + 153t + -16t2 + -3 + -153t + 16t2 Reorder the terms: 310 + -153t + 16t2 = 3 + -3 + 153t + -153t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 310 + -153t + 16t2 = 0 + 153t + -153t + -16t2 + 16t2 310 + -153t + 16t2 = 153t + -153t + -16t2 + 16t2 Combine like terms: 153t + -153t = 0 310 + -153t + 16t2 = 0 + -16t2 + 16t2 310 + -153t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 310 + -153t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 19.375 + -9.5625t + t2 = 0 Move the constant term to the right: Add '-19.375' to each side of the equation. 19.375 + -9.5625t + -19.375 + t2 = 0 + -19.375 Reorder the terms: 19.375 + -19.375 + -9.5625t + t2 = 0 + -19.375 Combine like terms: 19.375 + -19.375 = 0.000 0.000 + -9.5625t + t2 = 0 + -19.375 -9.5625t + t2 = 0 + -19.375 Combine like terms: 0 + -19.375 = -19.375 -9.5625t + t2 = -19.375 The t term is -9.5625t. Take half its coefficient (-4.78125). Square it (22.86035156) and add it to both sides. Add '22.86035156' to each side of the equation. -9.5625t + 22.86035156 + t2 = -19.375 + 22.86035156 Reorder the terms: 22.86035156 + -9.5625t + t2 = -19.375 + 22.86035156 Combine like terms: -19.375 + 22.86035156 = 3.48535156 22.86035156 + -9.5625t + t2 = 3.48535156 Factor a perfect square on the left side: (t + -4.78125)(t + -4.78125) = 3.48535156 Calculate the square root of the right side: 1.866909628 Break this problem into two subproblems by setting (t + -4.78125) equal to 1.866909628 and -1.866909628.Subproblem 1
t + -4.78125 = 1.866909628 Simplifying t + -4.78125 = 1.866909628 Reorder the terms: -4.78125 + t = 1.866909628 Solving -4.78125 + t = 1.866909628 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.78125' to each side of the equation. -4.78125 + 4.78125 + t = 1.866909628 + 4.78125 Combine like terms: -4.78125 + 4.78125 = 0.00000 0.00000 + t = 1.866909628 + 4.78125 t = 1.866909628 + 4.78125 Combine like terms: 1.866909628 + 4.78125 = 6.648159628 t = 6.648159628 Simplifying t = 6.648159628Subproblem 2
t + -4.78125 = -1.866909628 Simplifying t + -4.78125 = -1.866909628 Reorder the terms: -4.78125 + t = -1.866909628 Solving -4.78125 + t = -1.866909628 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.78125' to each side of the equation. -4.78125 + 4.78125 + t = -1.866909628 + 4.78125 Combine like terms: -4.78125 + 4.78125 = 0.00000 0.00000 + t = -1.866909628 + 4.78125 t = -1.866909628 + 4.78125 Combine like terms: -1.866909628 + 4.78125 = 2.914340372 t = 2.914340372 Simplifying t = 2.914340372Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.648159628, 2.914340372}
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