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Simplifying -0.07t2 + 0.84t + 1.5 = 0 Reorder the terms: 1.5 + 0.84t + -0.07t2 = 0 Solving 1.5 + 0.84t + -0.07t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.07 the coefficient of the squared term: Divide each side by '-0.07'. -21.42857143 + -12t + t2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -12t + 21.42857143 + t2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -12t + t2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -12t + t2 = 0 + 21.42857143 -12t + t2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -12t + t2 = 21.42857143 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 21.42857143 + 36 Reorder the terms: 36 + -12t + t2 = 21.42857143 + 36 Combine like terms: 21.42857143 + 36 = 57.42857143 36 + -12t + t2 = 57.42857143 Factor a perfect square on the left side: (t + -6)(t + -6) = 57.42857143 Calculate the square root of the right side: 7.57816412 Break this problem into two subproblems by setting (t + -6) equal to 7.57816412 and -7.57816412.Subproblem 1
t + -6 = 7.57816412 Simplifying t + -6 = 7.57816412 Reorder the terms: -6 + t = 7.57816412 Solving -6 + t = 7.57816412 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 7.57816412 + 6 Combine like terms: -6 + 6 = 0 0 + t = 7.57816412 + 6 t = 7.57816412 + 6 Combine like terms: 7.57816412 + 6 = 13.57816412 t = 13.57816412 Simplifying t = 13.57816412Subproblem 2
t + -6 = -7.57816412 Simplifying t + -6 = -7.57816412 Reorder the terms: -6 + t = -7.57816412 Solving -6 + t = -7.57816412 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -7.57816412 + 6 Combine like terms: -6 + 6 = 0 0 + t = -7.57816412 + 6 t = -7.57816412 + 6 Combine like terms: -7.57816412 + 6 = -1.57816412 t = -1.57816412 Simplifying t = -1.57816412Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.57816412, -1.57816412}
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