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Simplifying -4.905t2 + 10t + 20 = 0 Reorder the terms: 20 + 10t + -4.905t2 = 0 Solving 20 + 10t + -4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -4.077471967 + -2.038735984t + t2 = 0 Move the constant term to the right: Add '4.077471967' to each side of the equation. -4.077471967 + -2.038735984t + 4.077471967 + t2 = 0 + 4.077471967 Reorder the terms: -4.077471967 + 4.077471967 + -2.038735984t + t2 = 0 + 4.077471967 Combine like terms: -4.077471967 + 4.077471967 = 0.000000000 0.000000000 + -2.038735984t + t2 = 0 + 4.077471967 -2.038735984t + t2 = 0 + 4.077471967 Combine like terms: 0 + 4.077471967 = 4.077471967 -2.038735984t + t2 = 4.077471967 The t term is -2.038735984t. Take half its coefficient (-1.019367992). Square it (1.039111103) and add it to both sides. Add '1.039111103' to each side of the equation. -2.038735984t + 1.039111103 + t2 = 4.077471967 + 1.039111103 Reorder the terms: 1.039111103 + -2.038735984t + t2 = 4.077471967 + 1.039111103 Combine like terms: 4.077471967 + 1.039111103 = 5.11658307 1.039111103 + -2.038735984t + t2 = 5.11658307 Factor a perfect square on the left side: (t + -1.019367992)(t + -1.019367992) = 5.11658307 Calculate the square root of the right side: 2.261986532 Break this problem into two subproblems by setting (t + -1.019367992) equal to 2.261986532 and -2.261986532.Subproblem 1
t + -1.019367992 = 2.261986532 Simplifying t + -1.019367992 = 2.261986532 Reorder the terms: -1.019367992 + t = 2.261986532 Solving -1.019367992 + t = 2.261986532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.019367992' to each side of the equation. -1.019367992 + 1.019367992 + t = 2.261986532 + 1.019367992 Combine like terms: -1.019367992 + 1.019367992 = 0.000000000 0.000000000 + t = 2.261986532 + 1.019367992 t = 2.261986532 + 1.019367992 Combine like terms: 2.261986532 + 1.019367992 = 3.281354524 t = 3.281354524 Simplifying t = 3.281354524Subproblem 2
t + -1.019367992 = -2.261986532 Simplifying t + -1.019367992 = -2.261986532 Reorder the terms: -1.019367992 + t = -2.261986532 Solving -1.019367992 + t = -2.261986532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.019367992' to each side of the equation. -1.019367992 + 1.019367992 + t = -2.261986532 + 1.019367992 Combine like terms: -1.019367992 + 1.019367992 = 0.000000000 0.000000000 + t = -2.261986532 + 1.019367992 t = -2.261986532 + 1.019367992 Combine like terms: -2.261986532 + 1.019367992 = -1.24261854 t = -1.24261854 Simplifying t = -1.24261854Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.281354524, -1.24261854}
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