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Simplifying 20 = 26 + 9t + -4.9t2 Solving 20 = 26 + 9t + -4.9t2 Solving for variable 't'. Combine like terms: 20 + -26 = -6 -6 + -9t + 4.9t2 = 26 + 9t + -4.9t2 + -26 + -9t + 4.9t2 Reorder the terms: -6 + -9t + 4.9t2 = 26 + -26 + 9t + -9t + -4.9t2 + 4.9t2 Combine like terms: 26 + -26 = 0 -6 + -9t + 4.9t2 = 0 + 9t + -9t + -4.9t2 + 4.9t2 -6 + -9t + 4.9t2 = 9t + -9t + -4.9t2 + 4.9t2 Combine like terms: 9t + -9t = 0 -6 + -9t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -6 + -9t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -6 + -9t + 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'. -1.224489796 + -1.836734694t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -1.836734694t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -1.836734694t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -1.836734694t + t2 = 0 + 1.224489796 -1.836734694t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -1.836734694t + t2 = 1.224489796 The t term is -1.836734694t. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694t + 0.8433985840 + t2 = 1.224489796 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694t + t2 = 1.224489796 + 0.8433985840 Combine like terms: 1.224489796 + 0.8433985840 = 2.06788838 0.8433985840 + -1.836734694t + t2 = 2.06788838 Factor a perfect square on the left side: (t + -0.918367347)(t + -0.918367347) = 2.06788838 Calculate the square root of the right side: 1.438015431 Break this problem into two subproblems by setting (t + -0.918367347) equal to 1.438015431 and -1.438015431.Subproblem 1
t + -0.918367347 = 1.438015431 Simplifying t + -0.918367347 = 1.438015431 Reorder the terms: -0.918367347 + t = 1.438015431 Solving -0.918367347 + t = 1.438015431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + t = 1.438015431 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = 1.438015431 + 0.918367347 t = 1.438015431 + 0.918367347 Combine like terms: 1.438015431 + 0.918367347 = 2.356382778 t = 2.356382778 Simplifying t = 2.356382778Subproblem 2
t + -0.918367347 = -1.438015431 Simplifying t + -0.918367347 = -1.438015431 Reorder the terms: -0.918367347 + t = -1.438015431 Solving -0.918367347 + t = -1.438015431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + t = -1.438015431 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = -1.438015431 + 0.918367347 t = -1.438015431 + 0.918367347 Combine like terms: -1.438015431 + 0.918367347 = -0.519648084 t = -0.519648084 Simplifying t = -0.519648084Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.356382778, -0.519648084}
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