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Simplifying -0.25 = 2.37t + -4.90t2 Solving -0.25 = 2.37t + -4.90t2 Solving for variable 't'. Reorder the terms: -0.25 + -2.37t + 4.90t2 = 2.37t + -2.37t + -4.90t2 + 4.90t2 Combine like terms: 2.37t + -2.37t = 0.00 -0.25 + -2.37t + 4.90t2 = 0.00 + -4.90t2 + 4.90t2 -0.25 + -2.37t + 4.90t2 = -4.90t2 + 4.90t2 Combine like terms: -4.90t2 + 4.90t2 = 0.00 -0.25 + -2.37t + 4.90t2 = 0.00 Begin completing the square. Divide all terms by 4.90 the coefficient of the squared term: Divide each side by '4.90'. -0.05102040816 + -0.4836734694t + t2 = 0 Move the constant term to the right: Add '0.05102040816' to each side of the equation. -0.05102040816 + -0.4836734694t + 0.05102040816 + t2 = 0 + 0.05102040816 Reorder the terms: -0.05102040816 + 0.05102040816 + -0.4836734694t + t2 = 0 + 0.05102040816 Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000 0.00000000000 + -0.4836734694t + t2 = 0 + 0.05102040816 -0.4836734694t + t2 = 0 + 0.05102040816 Combine like terms: 0 + 0.05102040816 = 0.05102040816 -0.4836734694t + t2 = 0.05102040816 The t term is -0.4836734694t. Take half its coefficient (-0.2418367347). Square it (0.05848500625) and add it to both sides. Add '0.05848500625' to each side of the equation. -0.4836734694t + 0.05848500625 + t2 = 0.05102040816 + 0.05848500625 Reorder the terms: 0.05848500625 + -0.4836734694t + t2 = 0.05102040816 + 0.05848500625 Combine like terms: 0.05102040816 + 0.05848500625 = 0.10950541441 0.05848500625 + -0.4836734694t + t2 = 0.10950541441 Factor a perfect square on the left side: (t + -0.2418367347)(t + -0.2418367347) = 0.10950541441 Calculate the square root of the right side: 0.330916023 Break this problem into two subproblems by setting (t + -0.2418367347) equal to 0.330916023 and -0.330916023.Subproblem 1
t + -0.2418367347 = 0.330916023 Simplifying t + -0.2418367347 = 0.330916023 Reorder the terms: -0.2418367347 + t = 0.330916023 Solving -0.2418367347 + t = 0.330916023 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2418367347' to each side of the equation. -0.2418367347 + 0.2418367347 + t = 0.330916023 + 0.2418367347 Combine like terms: -0.2418367347 + 0.2418367347 = 0.0000000000 0.0000000000 + t = 0.330916023 + 0.2418367347 t = 0.330916023 + 0.2418367347 Combine like terms: 0.330916023 + 0.2418367347 = 0.5727527577 t = 0.5727527577 Simplifying t = 0.5727527577Subproblem 2
t + -0.2418367347 = -0.330916023 Simplifying t + -0.2418367347 = -0.330916023 Reorder the terms: -0.2418367347 + t = -0.330916023 Solving -0.2418367347 + t = -0.330916023 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2418367347' to each side of the equation. -0.2418367347 + 0.2418367347 + t = -0.330916023 + 0.2418367347 Combine like terms: -0.2418367347 + 0.2418367347 = 0.0000000000 0.0000000000 + t = -0.330916023 + 0.2418367347 t = -0.330916023 + 0.2418367347 Combine like terms: -0.330916023 + 0.2418367347 = -0.0890792883 t = -0.0890792883 Simplifying t = -0.0890792883Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5727527577, -0.0890792883}
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