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Simplifying -5t2 + 14t + 4 = 0 Reorder the terms: 4 + 14t + -5t2 = 0 Solving 4 + 14t + -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 + -2.8t + t2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2.8t + 0.8 + t2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2.8t + t2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2.8t + t2 = 0 + 0.8 -2.8t + t2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2.8t + t2 = 0.8 The t term is -2.8t. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8t + 1.96 + t2 = 0.8 + 1.96 Reorder the terms: 1.96 + -2.8t + t2 = 0.8 + 1.96 Combine like terms: 0.8 + 1.96 = 2.76 1.96 + -2.8t + t2 = 2.76 Factor a perfect square on the left side: (t + -1.4)(t + -1.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (t + -1.4) equal to 1.661324773 and -1.661324773.Subproblem 1
t + -1.4 = 1.661324773 Simplifying t + -1.4 = 1.661324773 Reorder the terms: -1.4 + t = 1.661324773 Solving -1.4 + t = 1.661324773 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = 1.661324773 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = 1.661324773 + 1.4 t = 1.661324773 + 1.4 Combine like terms: 1.661324773 + 1.4 = 3.061324773 t = 3.061324773 Simplifying t = 3.061324773Subproblem 2
t + -1.4 = -1.661324773 Simplifying t + -1.4 = -1.661324773 Reorder the terms: -1.4 + t = -1.661324773 Solving -1.4 + t = -1.661324773 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = -1.661324773 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = -1.661324773 + 1.4 t = -1.661324773 + 1.4 Combine like terms: -1.661324773 + 1.4 = -0.261324773 t = -0.261324773 Simplifying t = -0.261324773Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.061324773, -0.261324773}
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