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Simplifying 20t2 + 30t + -8 = 0 Reorder the terms: -8 + 30t + 20t2 = 0 Solving -8 + 30t + 20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 15t + 10t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 15t + 10t2)' equal to zero and attempt to solve: Simplifying -4 + 15t + 10t2 = 0 Solving -4 + 15t + 10t2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 1.5t + t2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.5t + 0.4 + t2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.5t + t2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.5t + t2 = 0.0 + 0.4 1.5t + t2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 1.5t + t2 = 0.4 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = 0.4 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = 0.4 + 0.5625 Combine like terms: 0.4 + 0.5625 = 0.9625 0.5625 + 1.5t + t2 = 0.9625 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 0.9625 Calculate the square root of the right side: 0.981070844 Break this problem into two subproblems by setting (t + 0.75) equal to 0.981070844 and -0.981070844.Subproblem 1
t + 0.75 = 0.981070844 Simplifying t + 0.75 = 0.981070844 Reorder the terms: 0.75 + t = 0.981070844 Solving 0.75 + t = 0.981070844 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = 0.981070844 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 0.981070844 + -0.75 t = 0.981070844 + -0.75 Combine like terms: 0.981070844 + -0.75 = 0.231070844 t = 0.231070844 Simplifying t = 0.231070844Subproblem 2
t + 0.75 = -0.981070844 Simplifying t + 0.75 = -0.981070844 Reorder the terms: 0.75 + t = -0.981070844 Solving 0.75 + t = -0.981070844 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = -0.981070844 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -0.981070844 + -0.75 t = -0.981070844 + -0.75 Combine like terms: -0.981070844 + -0.75 = -1.731070844 t = -1.731070844 Simplifying t = -1.731070844Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.231070844, -1.731070844}Solution
t = {0.231070844, -1.731070844}
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