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Simplifying 0 = -16t2 + 135t + 7 Reorder the terms: 0 = 7 + 135t + -16t2 Solving 0 = 7 + 135t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + -135t + 16t2 = 7 + 135t + -16t2 + -7 + -135t + 16t2 Reorder the terms: -7 + -135t + 16t2 = 7 + -7 + 135t + -135t + -16t2 + 16t2 Combine like terms: 7 + -7 = 0 -7 + -135t + 16t2 = 0 + 135t + -135t + -16t2 + 16t2 -7 + -135t + 16t2 = 135t + -135t + -16t2 + 16t2 Combine like terms: 135t + -135t = 0 -7 + -135t + 16t2 = 0 + -16t2 + 16t2 -7 + -135t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + -135t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -8.4375t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -8.4375t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -8.4375t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -8.4375t + t2 = 0 + 0.4375 -8.4375t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -8.4375t + t2 = 0.4375 The t term is -8.4375t. Take half its coefficient (-4.21875). Square it (17.79785156) and add it to both sides. Add '17.79785156' to each side of the equation. -8.4375t + 17.79785156 + t2 = 0.4375 + 17.79785156 Reorder the terms: 17.79785156 + -8.4375t + t2 = 0.4375 + 17.79785156 Combine like terms: 0.4375 + 17.79785156 = 18.23535156 17.79785156 + -8.4375t + t2 = 18.23535156 Factor a perfect square on the left side: (t + -4.21875)(t + -4.21875) = 18.23535156 Calculate the square root of the right side: 4.270287058 Break this problem into two subproblems by setting (t + -4.21875) equal to 4.270287058 and -4.270287058.Subproblem 1
t + -4.21875 = 4.270287058 Simplifying t + -4.21875 = 4.270287058 Reorder the terms: -4.21875 + t = 4.270287058 Solving -4.21875 + t = 4.270287058 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + t = 4.270287058 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + t = 4.270287058 + 4.21875 t = 4.270287058 + 4.21875 Combine like terms: 4.270287058 + 4.21875 = 8.489037058 t = 8.489037058 Simplifying t = 8.489037058Subproblem 2
t + -4.21875 = -4.270287058 Simplifying t + -4.21875 = -4.270287058 Reorder the terms: -4.21875 + t = -4.270287058 Solving -4.21875 + t = -4.270287058 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + t = -4.270287058 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + t = -4.270287058 + 4.21875 t = -4.270287058 + 4.21875 Combine like terms: -4.270287058 + 4.21875 = -0.051537058 t = -0.051537058 Simplifying t = -0.051537058Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.489037058, -0.051537058}
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