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Simplifying 100 = 15t + 5t2 Solving 100 = 15t + 5t2 Solving for variable 't'. Reorder the terms: 100 + -15t + -5t2 = 15t + -15t + 5t2 + -5t2 Combine like terms: 15t + -15t = 0 100 + -15t + -5t2 = 0 + 5t2 + -5t2 100 + -15t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 100 + -15t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(20 + -3t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + -3t + -1t2)' equal to zero and attempt to solve: Simplifying 20 + -3t + -1t2 = 0 Solving 20 + -3t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 3t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 3t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + 3t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3t + t2 = 0 + 20 3t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 3t + t2 = 20 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 20 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 20 + 2.25 Combine like terms: 20 + 2.25 = 22.25 2.25 + 3t + t2 = 22.25 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (t + 1.5) equal to 4.716990566 and -4.716990566.Subproblem 1
t + 1.5 = 4.716990566 Simplifying t + 1.5 = 4.716990566 Reorder the terms: 1.5 + t = 4.716990566 Solving 1.5 + t = 4.716990566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 4.716990566 + -1.5 t = 4.716990566 + -1.5 Combine like terms: 4.716990566 + -1.5 = 3.216990566 t = 3.216990566 Simplifying t = 3.216990566Subproblem 2
t + 1.5 = -4.716990566 Simplifying t + 1.5 = -4.716990566 Reorder the terms: 1.5 + t = -4.716990566 Solving 1.5 + t = -4.716990566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -4.716990566 + -1.5 t = -4.716990566 + -1.5 Combine like terms: -4.716990566 + -1.5 = -6.216990566 t = -6.216990566 Simplifying t = -6.216990566Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.216990566, -6.216990566}Solution
t = {3.216990566, -6.216990566}
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