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Simplifying 5t2 + 30t + 10 = 0 Reorder the terms: 10 + 30t + 5t2 = 0 Solving 10 + 30t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 6t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + 6t + t2)' equal to zero and attempt to solve: Simplifying 2 + 6t + t2 = 0 Solving 2 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 6t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6t + t2 = 0 + -2 6t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 6t + t2 = -2 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = -2 + 9 Reorder the terms: 9 + 6t + t2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6t + t2 = 7 Factor a perfect square on the left side: (t + 3)(t + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
t + 3 = 2.645751311 Simplifying t + 3 = 2.645751311 Reorder the terms: 3 + t = 2.645751311 Solving 3 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.645751311 + -3 t = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 t = -0.354248689 Simplifying t = -0.354248689Subproblem 2
t + 3 = -2.645751311 Simplifying t + 3 = -2.645751311 Reorder the terms: 3 + t = -2.645751311 Solving 3 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.645751311 + -3 t = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 t = -5.645751311 Simplifying t = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.354248689, -5.645751311}Solution
t = {-0.354248689, -5.645751311}
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