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Simplifying 2t + -2 = 5t(t + 2) Reorder the terms: -2 + 2t = 5t(t + 2) Reorder the terms: -2 + 2t = 5t(2 + t) -2 + 2t = (2 * 5t + t * 5t) -2 + 2t = (10t + 5t2) Solving -2 + 2t = 10t + 5t2 Solving for variable 't'. Combine like terms: 2t + -10t = -8t -2 + -8t + -5t2 = 10t + 5t2 + -10t + -5t2 Reorder the terms: -2 + -8t + -5t2 = 10t + -10t + 5t2 + -5t2 Combine like terms: 10t + -10t = 0 -2 + -8t + -5t2 = 0 + 5t2 + -5t2 -2 + -8t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -2 + -8t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 8t + 5t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 8t + 5t2)' equal to zero and attempt to solve: Simplifying 2 + 8t + 5t2 = 0 Solving 2 + 8t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.6t + t2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.6t + -0.4 + t2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.6t + t2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.6t + t2 = 0 + -0.4 1.6t + t2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.6t + t2 = -0.4 The t term is 1.6t. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6t + 0.64 + t2 = -0.4 + 0.64 Reorder the terms: 0.64 + 1.6t + t2 = -0.4 + 0.64 Combine like terms: -0.4 + 0.64 = 0.24 0.64 + 1.6t + t2 = 0.24 Factor a perfect square on the left side: (t + 0.8)(t + 0.8) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (t + 0.8) equal to 0.489897949 and -0.489897949.Subproblem 1
t + 0.8 = 0.489897949 Simplifying t + 0.8 = 0.489897949 Reorder the terms: 0.8 + t = 0.489897949 Solving 0.8 + t = 0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = 0.489897949 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = 0.489897949 + -0.8 t = 0.489897949 + -0.8 Combine like terms: 0.489897949 + -0.8 = -0.310102051 t = -0.310102051 Simplifying t = -0.310102051Subproblem 2
t + 0.8 = -0.489897949 Simplifying t + 0.8 = -0.489897949 Reorder the terms: 0.8 + t = -0.489897949 Solving 0.8 + t = -0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = -0.489897949 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = -0.489897949 + -0.8 t = -0.489897949 + -0.8 Combine like terms: -0.489897949 + -0.8 = -1.289897949 t = -1.289897949 Simplifying t = -1.289897949Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.310102051, -1.289897949}Solution
t = {-0.310102051, -1.289897949}
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