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Simplifying 10 = 4.9t2 + 2.29t Reorder the terms: 10 = 2.29t + 4.9t2 Solving 10 = 2.29t + 4.9t2 Solving for variable 't'. Reorder the terms: 10 + -2.29t + -4.9t2 = 2.29t + -2.29t + 4.9t2 + -4.9t2 Combine like terms: 2.29t + -2.29t = 0.00 10 + -2.29t + -4.9t2 = 0.00 + 4.9t2 + -4.9t2 10 + -2.29t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 10 + -2.29t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + 0.4673469388t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 0.4673469388t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 0.4673469388t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 0.4673469388t + t2 = 0 + 2.040816327 0.4673469388t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 0.4673469388t + t2 = 2.040816327 The t term is 0.4673469388t. Take half its coefficient (0.2336734694). Square it (0.05460329030) and add it to both sides. Add '0.05460329030' to each side of the equation. 0.4673469388t + 0.05460329030 + t2 = 2.040816327 + 0.05460329030 Reorder the terms: 0.05460329030 + 0.4673469388t + t2 = 2.040816327 + 0.05460329030 Combine like terms: 2.040816327 + 0.05460329030 = 2.0954196173 0.05460329030 + 0.4673469388t + t2 = 2.0954196173 Factor a perfect square on the left side: (t + 0.2336734694)(t + 0.2336734694) = 2.0954196173 Calculate the square root of the right side: 1.44755643 Break this problem into two subproblems by setting (t + 0.2336734694) equal to 1.44755643 and -1.44755643.Subproblem 1
t + 0.2336734694 = 1.44755643 Simplifying t + 0.2336734694 = 1.44755643 Reorder the terms: 0.2336734694 + t = 1.44755643 Solving 0.2336734694 + t = 1.44755643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2336734694' to each side of the equation. 0.2336734694 + -0.2336734694 + t = 1.44755643 + -0.2336734694 Combine like terms: 0.2336734694 + -0.2336734694 = 0.0000000000 0.0000000000 + t = 1.44755643 + -0.2336734694 t = 1.44755643 + -0.2336734694 Combine like terms: 1.44755643 + -0.2336734694 = 1.2138829606 t = 1.2138829606 Simplifying t = 1.2138829606Subproblem 2
t + 0.2336734694 = -1.44755643 Simplifying t + 0.2336734694 = -1.44755643 Reorder the terms: 0.2336734694 + t = -1.44755643 Solving 0.2336734694 + t = -1.44755643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2336734694' to each side of the equation. 0.2336734694 + -0.2336734694 + t = -1.44755643 + -0.2336734694 Combine like terms: 0.2336734694 + -0.2336734694 = 0.0000000000 0.0000000000 + t = -1.44755643 + -0.2336734694 t = -1.44755643 + -0.2336734694 Combine like terms: -1.44755643 + -0.2336734694 = -1.6812298994 t = -1.6812298994 Simplifying t = -1.6812298994Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2138829606, -1.6812298994}
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