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Simplifying -15t2 + 128t + 144 = 0 Reorder the terms: 144 + 128t + -15t2 = 0 Solving 144 + 128t + -15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -9.6 + -8.533333333t + t2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -8.533333333t + 9.6 + t2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -8.533333333t + t2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -8.533333333t + t2 = 0 + 9.6 -8.533333333t + t2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -8.533333333t + t2 = 9.6 The t term is -8.533333333t. Take half its coefficient (-4.266666667). Square it (18.20444445) and add it to both sides. Add '18.20444445' to each side of the equation. -8.533333333t + 18.20444445 + t2 = 9.6 + 18.20444445 Reorder the terms: 18.20444445 + -8.533333333t + t2 = 9.6 + 18.20444445 Combine like terms: 9.6 + 18.20444445 = 27.80444445 18.20444445 + -8.533333333t + t2 = 27.80444445 Factor a perfect square on the left side: (t + -4.266666667)(t + -4.266666667) = 27.80444445 Calculate the square root of the right side: 5.272991983 Break this problem into two subproblems by setting (t + -4.266666667) equal to 5.272991983 and -5.272991983.Subproblem 1
t + -4.266666667 = 5.272991983 Simplifying t + -4.266666667 = 5.272991983 Reorder the terms: -4.266666667 + t = 5.272991983 Solving -4.266666667 + t = 5.272991983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.266666667' to each side of the equation. -4.266666667 + 4.266666667 + t = 5.272991983 + 4.266666667 Combine like terms: -4.266666667 + 4.266666667 = 0.000000000 0.000000000 + t = 5.272991983 + 4.266666667 t = 5.272991983 + 4.266666667 Combine like terms: 5.272991983 + 4.266666667 = 9.53965865 t = 9.53965865 Simplifying t = 9.53965865Subproblem 2
t + -4.266666667 = -5.272991983 Simplifying t + -4.266666667 = -5.272991983 Reorder the terms: -4.266666667 + t = -5.272991983 Solving -4.266666667 + t = -5.272991983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.266666667' to each side of the equation. -4.266666667 + 4.266666667 + t = -5.272991983 + 4.266666667 Combine like terms: -4.266666667 + 4.266666667 = 0.000000000 0.000000000 + t = -5.272991983 + 4.266666667 t = -5.272991983 + 4.266666667 Combine like terms: -5.272991983 + 4.266666667 = -1.006325316 t = -1.006325316 Simplifying t = -1.006325316Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.53965865, -1.006325316}
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