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Simplifying (-5t2) + 4.9t + 45 = 0 Reorder the terms: 45 + 4.9t + (-5t2) = 0 Solving 45 + 4.9t + (-5t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9 + -0.98t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.98t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -0.98t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.98t + t2 = 0 + 9 -0.98t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.98t + t2 = 9 The t term is -0.98t. Take half its coefficient (-0.49). Square it (0.2401) and add it to both sides. Add '0.2401' to each side of the equation. -0.98t + 0.2401 + t2 = 9 + 0.2401 Reorder the terms: 0.2401 + -0.98t + t2 = 9 + 0.2401 Combine like terms: 9 + 0.2401 = 9.2401 0.2401 + -0.98t + t2 = 9.2401 Factor a perfect square on the left side: ((t) + -0.49)((t) + -0.49) = 9.2401 Calculate the square root of the right side: 3.039753279 Break this problem into two subproblems by setting ((t) + -0.49) equal to 3.039753279 and -3.039753279.Subproblem 1
(t) + -0.49 = 3.039753279 Simplifying (t) + -0.49 = 3.039753279 t + -0.49 = 3.039753279 Reorder the terms: -0.49 + t = 3.039753279 Solving -0.49 + t = 3.039753279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.49' to each side of the equation. -0.49 + 0.49 + t = 3.039753279 + 0.49 Combine like terms: -0.49 + 0.49 = 0.00 0.00 + t = 3.039753279 + 0.49 t = 3.039753279 + 0.49 Combine like terms: 3.039753279 + 0.49 = 3.529753279 t = 3.529753279 Simplifying t = 3.529753279Subproblem 2
(t) + -0.49 = -3.039753279 Simplifying (t) + -0.49 = -3.039753279 t + -0.49 = -3.039753279 Reorder the terms: -0.49 + t = -3.039753279 Solving -0.49 + t = -3.039753279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.49' to each side of the equation. -0.49 + 0.49 + t = -3.039753279 + 0.49 Combine like terms: -0.49 + 0.49 = 0.00 0.00 + t = -3.039753279 + 0.49 t = -3.039753279 + 0.49 Combine like terms: -3.039753279 + 0.49 = -2.549753279 t = -2.549753279 Simplifying t = -2.549753279Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.529753279, -2.549753279}
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