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Simplifying 30 = -4.9t2 + 14.7t + 75 Reorder the terms: 30 = 75 + 14.7t + -4.9t2 Solving 30 = 75 + 14.7t + -4.9t2 Solving for variable 't'. Combine like terms: 30 + -75 = -45 -45 + -14.7t + 4.9t2 = 75 + 14.7t + -4.9t2 + -75 + -14.7t + 4.9t2 Reorder the terms: -45 + -14.7t + 4.9t2 = 75 + -75 + 14.7t + -14.7t + -4.9t2 + 4.9t2 Combine like terms: 75 + -75 = 0 -45 + -14.7t + 4.9t2 = 0 + 14.7t + -14.7t + -4.9t2 + 4.9t2 -45 + -14.7t + 4.9t2 = 14.7t + -14.7t + -4.9t2 + 4.9t2 Combine like terms: 14.7t + -14.7t = 0.0 -45 + -14.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -45 + -14.7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -45 + -14.7t + 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'. -9.183673469 + -3t + t2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + -3t + 9.183673469 + t2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + -3t + t2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + -3t + t2 = 0 + 9.183673469 -3t + t2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 -3t + t2 = 9.183673469 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 9.183673469 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 9.183673469 + 2.25 Combine like terms: 9.183673469 + 2.25 = 11.433673469 2.25 + -3t + t2 = 11.433673469 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 11.433673469 Calculate the square root of the right side: 3.381371537 Break this problem into two subproblems by setting (t + -1.5) equal to 3.381371537 and -3.381371537.Subproblem 1
t + -1.5 = 3.381371537 Simplifying t + -1.5 = 3.381371537 Reorder the terms: -1.5 + t = 3.381371537 Solving -1.5 + t = 3.381371537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.381371537 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.381371537 + 1.5 t = 3.381371537 + 1.5 Combine like terms: 3.381371537 + 1.5 = 4.881371537 t = 4.881371537 Simplifying t = 4.881371537Subproblem 2
t + -1.5 = -3.381371537 Simplifying t + -1.5 = -3.381371537 Reorder the terms: -1.5 + t = -3.381371537 Solving -1.5 + t = -3.381371537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.381371537 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.381371537 + 1.5 t = -3.381371537 + 1.5 Combine like terms: -3.381371537 + 1.5 = -1.881371537 t = -1.881371537 Simplifying t = -1.881371537Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.881371537, -1.881371537}
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