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Simplifying 10t2 = 12t + 23 Reorder the terms: 10t2 = 23 + 12t Solving 10t2 = 23 + 12t Solving for variable 't'. Reorder the terms: -23 + -12t + 10t2 = 23 + 12t + -23 + -12t Reorder the terms: -23 + -12t + 10t2 = 23 + -23 + 12t + -12t Combine like terms: 23 + -23 = 0 -23 + -12t + 10t2 = 0 + 12t + -12t -23 + -12t + 10t2 = 12t + -12t Combine like terms: 12t + -12t = 0 -23 + -12t + 10t2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.3 + -1.2t + t2 = 0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + -1.2t + 2.3 + t2 = 0 + 2.3 Reorder the terms: -2.3 + 2.3 + -1.2t + t2 = 0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + -1.2t + t2 = 0 + 2.3 -1.2t + t2 = 0 + 2.3 Combine like terms: 0 + 2.3 = 2.3 -1.2t + t2 = 2.3 The t term is -1.2t. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2t + 0.36 + t2 = 2.3 + 0.36 Reorder the terms: 0.36 + -1.2t + t2 = 2.3 + 0.36 Combine like terms: 2.3 + 0.36 = 2.66 0.36 + -1.2t + t2 = 2.66 Factor a perfect square on the left side: (t + -0.6)(t + -0.6) = 2.66 Calculate the square root of the right side: 1.630950643 Break this problem into two subproblems by setting (t + -0.6) equal to 1.630950643 and -1.630950643.Subproblem 1
t + -0.6 = 1.630950643 Simplifying t + -0.6 = 1.630950643 Reorder the terms: -0.6 + t = 1.630950643 Solving -0.6 + t = 1.630950643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = 1.630950643 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = 1.630950643 + 0.6 t = 1.630950643 + 0.6 Combine like terms: 1.630950643 + 0.6 = 2.230950643 t = 2.230950643 Simplifying t = 2.230950643Subproblem 2
t + -0.6 = -1.630950643 Simplifying t + -0.6 = -1.630950643 Reorder the terms: -0.6 + t = -1.630950643 Solving -0.6 + t = -1.630950643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = -1.630950643 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = -1.630950643 + 0.6 t = -1.630950643 + 0.6 Combine like terms: -1.630950643 + 0.6 = -1.030950643 t = -1.030950643 Simplifying t = -1.030950643Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.230950643, -1.030950643}
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