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Simplifying -4.9t2 + 6t + 13 = 0 Reorder the terms: 13 + 6t + -4.9t2 = 0 Solving 13 + 6t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.653061224 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '2.653061224' to each side of the equation. -2.653061224 + -1.224489796t + 2.653061224 + t2 = 0 + 2.653061224 Reorder the terms: -2.653061224 + 2.653061224 + -1.224489796t + t2 = 0 + 2.653061224 Combine like terms: -2.653061224 + 2.653061224 = 0.000000000 0.000000000 + -1.224489796t + t2 = 0 + 2.653061224 -1.224489796t + t2 = 0 + 2.653061224 Combine like terms: 0 + 2.653061224 = 2.653061224 -1.224489796t + t2 = 2.653061224 The t term is -1.224489796t. Take half its coefficient (-0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. -1.224489796t + 0.3748438151 + t2 = 2.653061224 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 2.653061224 + 0.3748438151 Combine like terms: 2.653061224 + 0.3748438151 = 3.0279050391 0.3748438151 + -1.224489796t + t2 = 3.0279050391 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 3.0279050391 Calculate the square root of the right side: 1.740087653 Break this problem into two subproblems by setting (t + -0.612244898) equal to 1.740087653 and -1.740087653.Subproblem 1
t + -0.612244898 = 1.740087653 Simplifying t + -0.612244898 = 1.740087653 Reorder the terms: -0.612244898 + t = 1.740087653 Solving -0.612244898 + t = 1.740087653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = 1.740087653 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 1.740087653 + 0.612244898 t = 1.740087653 + 0.612244898 Combine like terms: 1.740087653 + 0.612244898 = 2.352332551 t = 2.352332551 Simplifying t = 2.352332551Subproblem 2
t + -0.612244898 = -1.740087653 Simplifying t + -0.612244898 = -1.740087653 Reorder the terms: -0.612244898 + t = -1.740087653 Solving -0.612244898 + t = -1.740087653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = -1.740087653 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -1.740087653 + 0.612244898 t = -1.740087653 + 0.612244898 Combine like terms: -1.740087653 + 0.612244898 = -1.127842755 t = -1.127842755 Simplifying t = -1.127842755Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.352332551, -1.127842755}
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