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Simplifying 178 = 50t + 3t2 Solving 178 = 50t + 3t2 Solving for variable 't'. Reorder the terms: 178 + -50t + -3t2 = 50t + -50t + 3t2 + -3t2 Combine like terms: 50t + -50t = 0 178 + -50t + -3t2 = 0 + 3t2 + -3t2 178 + -50t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 178 + -50t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -59.33333333 + 16.66666667t + t2 = 0 Move the constant term to the right: Add '59.33333333' to each side of the equation. -59.33333333 + 16.66666667t + 59.33333333 + t2 = 0 + 59.33333333 Reorder the terms: -59.33333333 + 59.33333333 + 16.66666667t + t2 = 0 + 59.33333333 Combine like terms: -59.33333333 + 59.33333333 = 0.00000000 0.00000000 + 16.66666667t + t2 = 0 + 59.33333333 16.66666667t + t2 = 0 + 59.33333333 Combine like terms: 0 + 59.33333333 = 59.33333333 16.66666667t + t2 = 59.33333333 The t term is 16.66666667t. Take half its coefficient (8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. 16.66666667t + 69.44444447 + t2 = 59.33333333 + 69.44444447 Reorder the terms: 69.44444447 + 16.66666667t + t2 = 59.33333333 + 69.44444447 Combine like terms: 59.33333333 + 69.44444447 = 128.7777778 69.44444447 + 16.66666667t + t2 = 128.7777778 Factor a perfect square on the left side: (t + 8.333333335)(t + 8.333333335) = 128.7777778 Calculate the square root of the right side: 11.348029688 Break this problem into two subproblems by setting (t + 8.333333335) equal to 11.348029688 and -11.348029688.Subproblem 1
t + 8.333333335 = 11.348029688 Simplifying t + 8.333333335 = 11.348029688 Reorder the terms: 8.333333335 + t = 11.348029688 Solving 8.333333335 + t = 11.348029688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + t = 11.348029688 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + t = 11.348029688 + -8.333333335 t = 11.348029688 + -8.333333335 Combine like terms: 11.348029688 + -8.333333335 = 3.014696353 t = 3.014696353 Simplifying t = 3.014696353Subproblem 2
t + 8.333333335 = -11.348029688 Simplifying t + 8.333333335 = -11.348029688 Reorder the terms: 8.333333335 + t = -11.348029688 Solving 8.333333335 + t = -11.348029688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + t = -11.348029688 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + t = -11.348029688 + -8.333333335 t = -11.348029688 + -8.333333335 Combine like terms: -11.348029688 + -8.333333335 = -19.681363023 t = -19.681363023 Simplifying t = -19.681363023Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.014696353, -19.681363023}
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