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Simplifying -0.8t2 + 1.5t + 0.9 = 0 Reorder the terms: 0.9 + 1.5t + -0.8t2 = 0 Solving 0.9 + 1.5t + -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'. -1.125 + -1.875t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1.875t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1.875t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1.875t + t2 = 0 + 1.125 -1.875t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1.875t + t2 = 1.125 The t term is -1.875t. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875t + 0.87890625 + t2 = 1.125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 1.125 + 0.87890625 Combine like terms: 1.125 + 0.87890625 = 2.00390625 0.87890625 + -1.875t + t2 = 2.00390625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 2.00390625 Calculate the square root of the right side: 1.415593957 Break this problem into two subproblems by setting (t + -0.9375) equal to 1.415593957 and -1.415593957.Subproblem 1
t + -0.9375 = 1.415593957 Simplifying t + -0.9375 = 1.415593957 Reorder the terms: -0.9375 + t = 1.415593957 Solving -0.9375 + t = 1.415593957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = 1.415593957 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 1.415593957 + 0.9375 t = 1.415593957 + 0.9375 Combine like terms: 1.415593957 + 0.9375 = 2.353093957 t = 2.353093957 Simplifying t = 2.353093957Subproblem 2
t + -0.9375 = -1.415593957 Simplifying t + -0.9375 = -1.415593957 Reorder the terms: -0.9375 + t = -1.415593957 Solving -0.9375 + t = -1.415593957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = -1.415593957 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -1.415593957 + 0.9375 t = -1.415593957 + 0.9375 Combine like terms: -1.415593957 + 0.9375 = -0.478093957 t = -0.478093957 Simplifying t = -0.478093957Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.353093957, -0.478093957}
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