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Simplifying 2 + 30t + -5t2 = 0 Solving 2 + 30t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -6t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -6t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -6t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -6t + t2 = 0 + 0.4 -6t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -6t + t2 = 0.4 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 = 0.4 + 9 Reorder the terms: 9 + -6t + t2 = 0.4 + 9 Combine like terms: 0.4 + 9 = 9.4 9 + -6t + t2 = 9.4 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.4 Calculate the square root of the right side: 3.065941943 Break this problem into two subproblems by setting (t + -3) equal to 3.065941943 and -3.065941943.Subproblem 1
t + -3 = 3.065941943 Simplifying t + -3 = 3.065941943 Reorder the terms: -3 + t = 3.065941943 Solving -3 + t = 3.065941943 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 = 3.065941943 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.065941943 + 3 t = 3.065941943 + 3 Combine like terms: 3.065941943 + 3 = 6.065941943 t = 6.065941943 Simplifying t = 6.065941943Subproblem 2
t + -3 = -3.065941943 Simplifying t + -3 = -3.065941943 Reorder the terms: -3 + t = -3.065941943 Solving -3 + t = -3.065941943 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 = -3.065941943 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.065941943 + 3 t = -3.065941943 + 3 Combine like terms: -3.065941943 + 3 = -0.065941943 t = -0.065941943 Simplifying t = -0.065941943Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.065941943, -0.065941943}
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