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Simplifying -5t2 + 40t + 4 = 0 Reorder the terms: 4 + 40t + -5t2 = 0 Solving 4 + 40t + -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'. -0.8 + -8t + t2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -8t + 0.8 + t2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -8t + t2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -8t + t2 = 0 + 0.8 -8t + t2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -8t + t2 = 0.8 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 0.8 + 16 Reorder the terms: 16 + -8t + t2 = 0.8 + 16 Combine like terms: 0.8 + 16 = 16.8 16 + -8t + t2 = 16.8 Factor a perfect square on the left side: (t + -4)(t + -4) = 16.8 Calculate the square root of the right side: 4.098780306 Break this problem into two subproblems by setting (t + -4) equal to 4.098780306 and -4.098780306.Subproblem 1
t + -4 = 4.098780306 Simplifying t + -4 = 4.098780306 Reorder the terms: -4 + t = 4.098780306 Solving -4 + t = 4.098780306 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.098780306 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.098780306 + 4 t = 4.098780306 + 4 Combine like terms: 4.098780306 + 4 = 8.098780306 t = 8.098780306 Simplifying t = 8.098780306Subproblem 2
t + -4 = -4.098780306 Simplifying t + -4 = -4.098780306 Reorder the terms: -4 + t = -4.098780306 Solving -4 + t = -4.098780306 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.098780306 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.098780306 + 4 t = -4.098780306 + 4 Combine like terms: -4.098780306 + 4 = -0.098780306 t = -0.098780306 Simplifying t = -0.098780306Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.098780306, -0.098780306}
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