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Simplifying -15t2 + 75t + 10 = 0 Reorder the terms: 10 + 75t + -15t2 = 0 Solving 10 + 75t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 15t + -3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + 15t + -3t2)' equal to zero and attempt to solve: Simplifying 2 + 15t + -3t2 = 0 Solving 2 + 15t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -5t + t2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -5t + 0.6666666667 + t2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -5t + t2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -5t + t2 = 0 + 0.6666666667 -5t + t2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -5t + t2 = 0.6666666667 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 = 0.6666666667 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 0.6666666667 + 6.25 Combine like terms: 0.6666666667 + 6.25 = 6.9166666667 6.25 + -5t + t2 = 6.9166666667 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 6.9166666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (t + -2.5) equal to 2.62995564 and -2.62995564.Subproblem 1
t + -2.5 = 2.62995564 Simplifying t + -2.5 = 2.62995564 Reorder the terms: -2.5 + t = 2.62995564 Solving -2.5 + t = 2.62995564 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 = 2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.62995564 + 2.5 t = 2.62995564 + 2.5 Combine like terms: 2.62995564 + 2.5 = 5.12995564 t = 5.12995564 Simplifying t = 5.12995564Subproblem 2
t + -2.5 = -2.62995564 Simplifying t + -2.5 = -2.62995564 Reorder the terms: -2.5 + t = -2.62995564 Solving -2.5 + t = -2.62995564 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 = -2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.62995564 + 2.5 t = -2.62995564 + 2.5 Combine like terms: -2.62995564 + 2.5 = -0.12995564 t = -0.12995564 Simplifying t = -0.12995564Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.12995564, -0.12995564}Solution
t = {5.12995564, -0.12995564}
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