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Simplifying 0.15t2 + -43t + 1000 = 0 Reorder the terms: 1000 + -43t + 0.15t2 = 0 Solving 1000 + -43t + 0.15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. 6666.666667 + -286.6666667t + t2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + -286.6666667t + -6666.666667 + t2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + -286.6666667t + t2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + -286.6666667t + t2 = 0 + -6666.666667 -286.6666667t + t2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 -286.6666667t + t2 = -6666.666667 The t term is -286.6666667t. Take half its coefficient (-143.3333334). Square it (20544.44446) and add it to both sides. Add '20544.44446' to each side of the equation. -286.6666667t + 20544.44446 + t2 = -6666.666667 + 20544.44446 Reorder the terms: 20544.44446 + -286.6666667t + t2 = -6666.666667 + 20544.44446 Combine like terms: -6666.666667 + 20544.44446 = 13877.777793 20544.44446 + -286.6666667t + t2 = 13877.777793 Factor a perfect square on the left side: (t + -143.3333334)(t + -143.3333334) = 13877.777793 Calculate the square root of the right side: 117.803980378 Break this problem into two subproblems by setting (t + -143.3333334) equal to 117.803980378 and -117.803980378.Subproblem 1
t + -143.3333334 = 117.803980378 Simplifying t + -143.3333334 = 117.803980378 Reorder the terms: -143.3333334 + t = 117.803980378 Solving -143.3333334 + t = 117.803980378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '143.3333334' to each side of the equation. -143.3333334 + 143.3333334 + t = 117.803980378 + 143.3333334 Combine like terms: -143.3333334 + 143.3333334 = 0.0000000 0.0000000 + t = 117.803980378 + 143.3333334 t = 117.803980378 + 143.3333334 Combine like terms: 117.803980378 + 143.3333334 = 261.137313778 t = 261.137313778 Simplifying t = 261.137313778Subproblem 2
t + -143.3333334 = -117.803980378 Simplifying t + -143.3333334 = -117.803980378 Reorder the terms: -143.3333334 + t = -117.803980378 Solving -143.3333334 + t = -117.803980378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '143.3333334' to each side of the equation. -143.3333334 + 143.3333334 + t = -117.803980378 + 143.3333334 Combine like terms: -143.3333334 + 143.3333334 = 0.0000000 0.0000000 + t = -117.803980378 + 143.3333334 t = -117.803980378 + 143.3333334 Combine like terms: -117.803980378 + 143.3333334 = 25.529353022 t = 25.529353022 Simplifying t = 25.529353022Solution
The solution to the problem is based on the solutions from the subproblems. t = {261.137313778, 25.529353022}
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