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Simplifying 1.5 + 19t + -0.8t2 = 0 Solving 1.5 + 19t + -0.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -1.875 + -23.75t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -23.75t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -23.75t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -23.75t + t2 = 0 + 1.875 -23.75t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -23.75t + t2 = 1.875 The t term is -23.75t. Take half its coefficient (-11.875). Square it (141.015625) and add it to both sides. Add '141.015625' to each side of the equation. -23.75t + 141.015625 + t2 = 1.875 + 141.015625 Reorder the terms: 141.015625 + -23.75t + t2 = 1.875 + 141.015625 Combine like terms: 1.875 + 141.015625 = 142.890625 141.015625 + -23.75t + t2 = 142.890625 Factor a perfect square on the left side: (t + -11.875)(t + -11.875) = 142.890625 Calculate the square root of the right side: 11.95368667 Break this problem into two subproblems by setting (t + -11.875) equal to 11.95368667 and -11.95368667.Subproblem 1
t + -11.875 = 11.95368667 Simplifying t + -11.875 = 11.95368667 Reorder the terms: -11.875 + t = 11.95368667 Solving -11.875 + t = 11.95368667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + t = 11.95368667 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + t = 11.95368667 + 11.875 t = 11.95368667 + 11.875 Combine like terms: 11.95368667 + 11.875 = 23.82868667 t = 23.82868667 Simplifying t = 23.82868667Subproblem 2
t + -11.875 = -11.95368667 Simplifying t + -11.875 = -11.95368667 Reorder the terms: -11.875 + t = -11.95368667 Solving -11.875 + t = -11.95368667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + t = -11.95368667 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + t = -11.95368667 + 11.875 t = -11.95368667 + 11.875 Combine like terms: -11.95368667 + 11.875 = -0.07868667 t = -0.07868667 Simplifying t = -0.07868667Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.82868667, -0.07868667}
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