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Simplifying 4.9t2 + -32t + -1.9 = 0 Reorder the terms: -1.9 + -32t + 4.9t2 = 0 Solving -1.9 + -32t + 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'. -0.387755102 + -6.530612245t + t2 = 0 Move the constant term to the right: Add '0.387755102' to each side of the equation. -0.387755102 + -6.530612245t + 0.387755102 + t2 = 0 + 0.387755102 Reorder the terms: -0.387755102 + 0.387755102 + -6.530612245t + t2 = 0 + 0.387755102 Combine like terms: -0.387755102 + 0.387755102 = 0.000000000 0.000000000 + -6.530612245t + t2 = 0 + 0.387755102 -6.530612245t + t2 = 0 + 0.387755102 Combine like terms: 0 + 0.387755102 = 0.387755102 -6.530612245t + t2 = 0.387755102 The t term is -6.530612245t. Take half its coefficient (-3.265306123). Square it (10.66222408) and add it to both sides. Add '10.66222408' to each side of the equation. -6.530612245t + 10.66222408 + t2 = 0.387755102 + 10.66222408 Reorder the terms: 10.66222408 + -6.530612245t + t2 = 0.387755102 + 10.66222408 Combine like terms: 0.387755102 + 10.66222408 = 11.049979182 10.66222408 + -6.530612245t + t2 = 11.049979182 Factor a perfect square on the left side: (t + -3.265306123)(t + -3.265306123) = 11.049979182 Calculate the square root of the right side: 3.324150896 Break this problem into two subproblems by setting (t + -3.265306123) equal to 3.324150896 and -3.324150896.Subproblem 1
t + -3.265306123 = 3.324150896 Simplifying t + -3.265306123 = 3.324150896 Reorder the terms: -3.265306123 + t = 3.324150896 Solving -3.265306123 + t = 3.324150896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = 3.324150896 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = 3.324150896 + 3.265306123 t = 3.324150896 + 3.265306123 Combine like terms: 3.324150896 + 3.265306123 = 6.589457019 t = 6.589457019 Simplifying t = 6.589457019Subproblem 2
t + -3.265306123 = -3.324150896 Simplifying t + -3.265306123 = -3.324150896 Reorder the terms: -3.265306123 + t = -3.324150896 Solving -3.265306123 + t = -3.324150896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = -3.324150896 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = -3.324150896 + 3.265306123 t = -3.324150896 + 3.265306123 Combine like terms: -3.324150896 + 3.265306123 = -0.058844773 t = -0.058844773 Simplifying t = -0.058844773Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.589457019, -0.058844773}
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