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Simplifying -4t2 + 9t + 10 = 0 Reorder the terms: 10 + 9t + -4t2 = 0 Solving 10 + 9t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + -2.25t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.25t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.25t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.25t + t2 = 0 + 2.5 -2.25t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.25t + t2 = 2.5 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 2.5 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 2.5 + 1.265625 Combine like terms: 2.5 + 1.265625 = 3.765625 1.265625 + -2.25t + t2 = 3.765625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (t + -1.125) equal to 1.940521837 and -1.940521837.Subproblem 1
t + -1.125 = 1.940521837 Simplifying t + -1.125 = 1.940521837 Reorder the terms: -1.125 + t = 1.940521837 Solving -1.125 + t = 1.940521837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.940521837 + 1.125 t = 1.940521837 + 1.125 Combine like terms: 1.940521837 + 1.125 = 3.065521837 t = 3.065521837 Simplifying t = 3.065521837Subproblem 2
t + -1.125 = -1.940521837 Simplifying t + -1.125 = -1.940521837 Reorder the terms: -1.125 + t = -1.940521837 Solving -1.125 + t = -1.940521837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.940521837 + 1.125 t = -1.940521837 + 1.125 Combine like terms: -1.940521837 + 1.125 = -0.815521837 t = -0.815521837 Simplifying t = -0.815521837Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.065521837, -0.815521837}
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