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Simplifying 200 = 6t + 0.75t2 Solving 200 = 6t + 0.75t2 Solving for variable 't'. Reorder the terms: 200 + -6t + -0.75t2 = 6t + -6t + 0.75t2 + -0.75t2 Combine like terms: 6t + -6t = 0 200 + -6t + -0.75t2 = 0 + 0.75t2 + -0.75t2 200 + -6t + -0.75t2 = 0.75t2 + -0.75t2 Combine like terms: 0.75t2 + -0.75t2 = 0.00 200 + -6t + -0.75t2 = 0.00 Begin completing the square. Divide all terms by -0.75 the coefficient of the squared term: Divide each side by '-0.75'. -266.6666667 + 8t + t2 = 0 Move the constant term to the right: Add '266.6666667' to each side of the equation. -266.6666667 + 8t + 266.6666667 + t2 = 0 + 266.6666667 Reorder the terms: -266.6666667 + 266.6666667 + 8t + t2 = 0 + 266.6666667 Combine like terms: -266.6666667 + 266.6666667 = 0.0000000 0.0000000 + 8t + t2 = 0 + 266.6666667 8t + t2 = 0 + 266.6666667 Combine like terms: 0 + 266.6666667 = 266.6666667 8t + t2 = 266.6666667 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 266.6666667 + 16 Reorder the terms: 16 + 8t + t2 = 266.6666667 + 16 Combine like terms: 266.6666667 + 16 = 282.6666667 16 + 8t + t2 = 282.6666667 Factor a perfect square on the left side: (t + 4)(t + 4) = 282.6666667 Calculate the square root of the right side: 16.812693618 Break this problem into two subproblems by setting (t + 4) equal to 16.812693618 and -16.812693618.Subproblem 1
t + 4 = 16.812693618 Simplifying t + 4 = 16.812693618 Reorder the terms: 4 + t = 16.812693618 Solving 4 + t = 16.812693618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 16.812693618 + -4 Combine like terms: 4 + -4 = 0 0 + t = 16.812693618 + -4 t = 16.812693618 + -4 Combine like terms: 16.812693618 + -4 = 12.812693618 t = 12.812693618 Simplifying t = 12.812693618Subproblem 2
t + 4 = -16.812693618 Simplifying t + 4 = -16.812693618 Reorder the terms: 4 + t = -16.812693618 Solving 4 + t = -16.812693618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -16.812693618 + -4 Combine like terms: 4 + -4 = 0 0 + t = -16.812693618 + -4 t = -16.812693618 + -4 Combine like terms: -16.812693618 + -4 = -20.812693618 t = -20.812693618 Simplifying t = -20.812693618Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.812693618, -20.812693618}
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