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Simplifying 19 = 18t + 5t2 Solving 19 = 18t + 5t2 Solving for variable 't'. Reorder the terms: 19 + -18t + -5t2 = 18t + -18t + 5t2 + -5t2 Combine like terms: 18t + -18t = 0 19 + -18t + -5t2 = 0 + 5t2 + -5t2 19 + -18t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 19 + -18t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.8 + 3.6t + t2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 3.6t + 3.8 + t2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 3.6t + t2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 3.6t + t2 = 0 + 3.8 3.6t + t2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 3.6t + t2 = 3.8 The t term is 3.6t. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6t + 3.24 + t2 = 3.8 + 3.24 Reorder the terms: 3.24 + 3.6t + t2 = 3.8 + 3.24 Combine like terms: 3.8 + 3.24 = 7.04 3.24 + 3.6t + t2 = 7.04 Factor a perfect square on the left side: (t + 1.8)(t + 1.8) = 7.04 Calculate the square root of the right side: 2.653299832 Break this problem into two subproblems by setting (t + 1.8) equal to 2.653299832 and -2.653299832.Subproblem 1
t + 1.8 = 2.653299832 Simplifying t + 1.8 = 2.653299832 Reorder the terms: 1.8 + t = 2.653299832 Solving 1.8 + t = 2.653299832 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + t = 2.653299832 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + t = 2.653299832 + -1.8 t = 2.653299832 + -1.8 Combine like terms: 2.653299832 + -1.8 = 0.853299832 t = 0.853299832 Simplifying t = 0.853299832Subproblem 2
t + 1.8 = -2.653299832 Simplifying t + 1.8 = -2.653299832 Reorder the terms: 1.8 + t = -2.653299832 Solving 1.8 + t = -2.653299832 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + t = -2.653299832 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + t = -2.653299832 + -1.8 t = -2.653299832 + -1.8 Combine like terms: -2.653299832 + -1.8 = -4.453299832 t = -4.453299832 Simplifying t = -4.453299832Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.853299832, -4.453299832}
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