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Simplifying -0.3t2 + 60t = -45 Reorder the terms: 60t + -0.3t2 = -45 Solving 60t + -0.3t2 = -45 Solving for variable 't'. Reorder the terms: 45 + 60t + -0.3t2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + 60t + -0.3t2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -150 + -200t + t2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -200t + 150 + t2 = 0 + 150 Reorder the terms: -150 + 150 + -200t + t2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -200t + t2 = 0 + 150 -200t + t2 = 0 + 150 Combine like terms: 0 + 150 = 150 -200t + t2 = 150 The t term is -200t. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200t + 10000 + t2 = 150 + 10000 Reorder the terms: 10000 + -200t + t2 = 150 + 10000 Combine like terms: 150 + 10000 = 10150 10000 + -200t + t2 = 10150 Factor a perfect square on the left side: (t + -100)(t + -100) = 10150 Calculate the square root of the right side: 100.747208398 Break this problem into two subproblems by setting (t + -100) equal to 100.747208398 and -100.747208398.Subproblem 1
t + -100 = 100.747208398 Simplifying t + -100 = 100.747208398 Reorder the terms: -100 + t = 100.747208398 Solving -100 + t = 100.747208398 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = 100.747208398 + 100 Combine like terms: -100 + 100 = 0 0 + t = 100.747208398 + 100 t = 100.747208398 + 100 Combine like terms: 100.747208398 + 100 = 200.747208398 t = 200.747208398 Simplifying t = 200.747208398Subproblem 2
t + -100 = -100.747208398 Simplifying t + -100 = -100.747208398 Reorder the terms: -100 + t = -100.747208398 Solving -100 + t = -100.747208398 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = -100.747208398 + 100 Combine like terms: -100 + 100 = 0 0 + t = -100.747208398 + 100 t = -100.747208398 + 100 Combine like terms: -100.747208398 + 100 = -0.747208398 t = -0.747208398 Simplifying t = -0.747208398Solution
The solution to the problem is based on the solutions from the subproblems. t = {200.747208398, -0.747208398}
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