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Simplifying 0 = -4.9t2 + 7.5t + 165 Reorder the terms: 0 = 165 + 7.5t + -4.9t2 Solving 0 = 165 + 7.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -165 = -165 -165 + -7.5t + 4.9t2 = 165 + 7.5t + -4.9t2 + -165 + -7.5t + 4.9t2 Reorder the terms: -165 + -7.5t + 4.9t2 = 165 + -165 + 7.5t + -7.5t + -4.9t2 + 4.9t2 Combine like terms: 165 + -165 = 0 -165 + -7.5t + 4.9t2 = 0 + 7.5t + -7.5t + -4.9t2 + 4.9t2 -165 + -7.5t + 4.9t2 = 7.5t + -7.5t + -4.9t2 + 4.9t2 Combine like terms: 7.5t + -7.5t = 0.0 -165 + -7.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -165 + -7.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -165 + -7.5t + 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'. -33.67346939 + -1.530612245t + t2 = 0 Move the constant term to the right: Add '33.67346939' to each side of the equation. -33.67346939 + -1.530612245t + 33.67346939 + t2 = 0 + 33.67346939 Reorder the terms: -33.67346939 + 33.67346939 + -1.530612245t + t2 = 0 + 33.67346939 Combine like terms: -33.67346939 + 33.67346939 = 0.00000000 0.00000000 + -1.530612245t + t2 = 0 + 33.67346939 -1.530612245t + t2 = 0 + 33.67346939 Combine like terms: 0 + 33.67346939 = 33.67346939 -1.530612245t + t2 = 33.67346939 The t term is -1.530612245t. Take half its coefficient (-0.7653061225). Square it (0.5856934611) and add it to both sides. Add '0.5856934611' to each side of the equation. -1.530612245t + 0.5856934611 + t2 = 33.67346939 + 0.5856934611 Reorder the terms: 0.5856934611 + -1.530612245t + t2 = 33.67346939 + 0.5856934611 Combine like terms: 33.67346939 + 0.5856934611 = 34.2591628511 0.5856934611 + -1.530612245t + t2 = 34.2591628511 Factor a perfect square on the left side: (t + -0.7653061225)(t + -0.7653061225) = 34.2591628511 Calculate the square root of the right side: 5.853132738 Break this problem into two subproblems by setting (t + -0.7653061225) equal to 5.853132738 and -5.853132738.Subproblem 1
t + -0.7653061225 = 5.853132738 Simplifying t + -0.7653061225 = 5.853132738 Reorder the terms: -0.7653061225 + t = 5.853132738 Solving -0.7653061225 + t = 5.853132738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7653061225' to each side of the equation. -0.7653061225 + 0.7653061225 + t = 5.853132738 + 0.7653061225 Combine like terms: -0.7653061225 + 0.7653061225 = 0.0000000000 0.0000000000 + t = 5.853132738 + 0.7653061225 t = 5.853132738 + 0.7653061225 Combine like terms: 5.853132738 + 0.7653061225 = 6.6184388605 t = 6.6184388605 Simplifying t = 6.6184388605Subproblem 2
t + -0.7653061225 = -5.853132738 Simplifying t + -0.7653061225 = -5.853132738 Reorder the terms: -0.7653061225 + t = -5.853132738 Solving -0.7653061225 + t = -5.853132738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7653061225' to each side of the equation. -0.7653061225 + 0.7653061225 + t = -5.853132738 + 0.7653061225 Combine like terms: -0.7653061225 + 0.7653061225 = 0.0000000000 0.0000000000 + t = -5.853132738 + 0.7653061225 t = -5.853132738 + 0.7653061225 Combine like terms: -5.853132738 + 0.7653061225 = -5.0878266155 t = -5.0878266155 Simplifying t = -5.0878266155Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.6184388605, -5.0878266155}
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