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Simplifying 1 = -4.9t2 + 3.5t + 10 Reorder the terms: 1 = 10 + 3.5t + -4.9t2 Solving 1 = 10 + 3.5t + -4.9t2 Solving for variable 't'. Combine like terms: 1 + -10 = -9 -9 + -3.5t + 4.9t2 = 10 + 3.5t + -4.9t2 + -10 + -3.5t + 4.9t2 Reorder the terms: -9 + -3.5t + 4.9t2 = 10 + -10 + 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -9 + -3.5t + 4.9t2 = 0 + 3.5t + -3.5t + -4.9t2 + 4.9t2 -9 + -3.5t + 4.9t2 = 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 3.5t + -3.5t = 0.0 -9 + -3.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -9 + -3.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -9 + -3.5t + 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'. -1.836734694 + -0.7142857143t + t2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + -0.7142857143t + 1.836734694 + t2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + -0.7142857143t + t2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + -0.7142857143t + t2 = 0 + 1.836734694 -0.7142857143t + t2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 -0.7142857143t + t2 = 1.836734694 The t term is -0.7142857143t. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143t + 0.1275510204 + t2 = 1.836734694 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143t + t2 = 1.836734694 + 0.1275510204 Combine like terms: 1.836734694 + 0.1275510204 = 1.9642857144 0.1275510204 + -0.7142857143t + t2 = 1.9642857144 Factor a perfect square on the left side: (t + -0.3571428572)(t + -0.3571428572) = 1.9642857144 Calculate the square root of the right side: 1.401529776 Break this problem into two subproblems by setting (t + -0.3571428572) equal to 1.401529776 and -1.401529776.Subproblem 1
t + -0.3571428572 = 1.401529776 Simplifying t + -0.3571428572 = 1.401529776 Reorder the terms: -0.3571428572 + t = 1.401529776 Solving -0.3571428572 + t = 1.401529776 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = 1.401529776 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = 1.401529776 + 0.3571428572 t = 1.401529776 + 0.3571428572 Combine like terms: 1.401529776 + 0.3571428572 = 1.7586726332 t = 1.7586726332 Simplifying t = 1.7586726332Subproblem 2
t + -0.3571428572 = -1.401529776 Simplifying t + -0.3571428572 = -1.401529776 Reorder the terms: -0.3571428572 + t = -1.401529776 Solving -0.3571428572 + t = -1.401529776 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = -1.401529776 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = -1.401529776 + 0.3571428572 t = -1.401529776 + 0.3571428572 Combine like terms: -1.401529776 + 0.3571428572 = -1.0443869188 t = -1.0443869188 Simplifying t = -1.0443869188Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7586726332, -1.0443869188}
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