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Simplifying 0.375t2 + 6t + -120 = 0 Reorder the terms: -120 + 6t + 0.375t2 = 0 Solving -120 + 6t + 0.375t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.375 the coefficient of the squared term: Divide each side by '0.375'. -320 + 16t + t2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + 16t + 320 + t2 = 0 + 320 Reorder the terms: -320 + 320 + 16t + t2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 16t + t2 = 0 + 320 16t + t2 = 0 + 320 Combine like terms: 0 + 320 = 320 16t + t2 = 320 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = 320 + 64 Reorder the terms: 64 + 16t + t2 = 320 + 64 Combine like terms: 320 + 64 = 384 64 + 16t + t2 = 384 Factor a perfect square on the left side: (t + 8)(t + 8) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (t + 8) equal to 19.595917942 and -19.595917942.Subproblem 1
t + 8 = 19.595917942 Simplifying t + 8 = 19.595917942 Reorder the terms: 8 + t = 19.595917942 Solving 8 + t = 19.595917942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 19.595917942 + -8 Combine like terms: 8 + -8 = 0 0 + t = 19.595917942 + -8 t = 19.595917942 + -8 Combine like terms: 19.595917942 + -8 = 11.595917942 t = 11.595917942 Simplifying t = 11.595917942Subproblem 2
t + 8 = -19.595917942 Simplifying t + 8 = -19.595917942 Reorder the terms: 8 + t = -19.595917942 Solving 8 + t = -19.595917942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -19.595917942 + -8 Combine like terms: 8 + -8 = 0 0 + t = -19.595917942 + -8 t = -19.595917942 + -8 Combine like terms: -19.595917942 + -8 = -27.595917942 t = -27.595917942 Simplifying t = -27.595917942Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.595917942, -27.595917942}
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