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Simplifying 15t2 + 75t + -60 = 0 Reorder the terms: -60 + 75t + 15t2 = 0 Solving -60 + 75t + 15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(-4 + 5t + t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + 5t + t2)' equal to zero and attempt to solve: Simplifying -4 + 5t + t2 = 0 Solving -4 + 5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5t + t2 = 0 + 4 5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 5t + t2 = 4 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 4 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5t + t2 = 10.25 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (t + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
t + 2.5 = 3.201562119 Simplifying t + 2.5 = 3.201562119 Reorder the terms: 2.5 + t = 3.201562119 Solving 2.5 + t = 3.201562119 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 3.201562119 + -2.5 t = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 t = 0.701562119 Simplifying t = 0.701562119Subproblem 2
t + 2.5 = -3.201562119 Simplifying t + 2.5 = -3.201562119 Reorder the terms: 2.5 + t = -3.201562119 Solving 2.5 + t = -3.201562119 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -3.201562119 + -2.5 t = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 t = -5.701562119 Simplifying t = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.701562119, -5.701562119}Solution
t = {0.701562119, -5.701562119}
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