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Simplifying 15t + -5 = t2 Reorder the terms: -5 + 15t = t2 Solving -5 + 15t = t2 Solving for variable 't'. Combine like terms: t2 + -1t2 = 0 -5 + 15t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -15t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -15t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -15t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -15t + t2 = 0 + -5 -15t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -15t + t2 = -5 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = -5 + 56.25 Reorder the terms: 56.25 + -15t + t2 = -5 + 56.25 Combine like terms: -5 + 56.25 = 51.25 56.25 + -15t + t2 = 51.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (t + -7.5) equal to 7.158910532 and -7.158910532.Subproblem 1
t + -7.5 = 7.158910532 Simplifying t + -7.5 = 7.158910532 Reorder the terms: -7.5 + t = 7.158910532 Solving -7.5 + t = 7.158910532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 7.158910532 + 7.5 t = 7.158910532 + 7.5 Combine like terms: 7.158910532 + 7.5 = 14.658910532 t = 14.658910532 Simplifying t = 14.658910532Subproblem 2
t + -7.5 = -7.158910532 Simplifying t + -7.5 = -7.158910532 Reorder the terms: -7.5 + t = -7.158910532 Solving -7.5 + t = -7.158910532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -7.158910532 + 7.5 t = -7.158910532 + 7.5 Combine like terms: -7.158910532 + 7.5 = 0.341089468 t = 0.341089468 Simplifying t = 0.341089468Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.658910532, 0.341089468}
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