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Simplifying 0.5(-9.8)(t)(t) + 250(t) + 10 = t Multiply 0.5 * -9.8 -4.9t * t + 250(t) + 10 = t Multiply t * t -4.9t2 + 250(t) + 10 = t Reorder the terms: 10 + 250t + -4.9t2 = t Solving 10 + 250t + -4.9t2 = t Solving for variable 't'. Reorder the terms: 10 + 250t + -1t + -4.9t2 = t + -1t Combine like terms: 250t + -1t = 249t 10 + 249t + -4.9t2 = t + -1t Combine like terms: t + -1t = 0 10 + 249t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + -50.81632653t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -50.81632653t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -50.81632653t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -50.81632653t + t2 = 0 + 2.040816327 -50.81632653t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -50.81632653t + t2 = 2.040816327 The t term is -50.81632653t. Take half its coefficient (-25.40816327). Square it (645.5747608) and add it to both sides. Add '645.5747608' to each side of the equation. -50.81632653t + 645.5747608 + t2 = 2.040816327 + 645.5747608 Reorder the terms: 645.5747608 + -50.81632653t + t2 = 2.040816327 + 645.5747608 Combine like terms: 2.040816327 + 645.5747608 = 647.615577127 645.5747608 + -50.81632653t + t2 = 647.615577127 Factor a perfect square on the left side: (t + -25.40816327)(t + -25.40816327) = 647.615577127 Calculate the square root of the right side: 25.448292224 Break this problem into two subproblems by setting (t + -25.40816327) equal to 25.448292224 and -25.448292224.Subproblem 1
t + -25.40816327 = 25.448292224 Simplifying t + -25.40816327 = 25.448292224 Reorder the terms: -25.40816327 + t = 25.448292224 Solving -25.40816327 + t = 25.448292224 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.40816327' to each side of the equation. -25.40816327 + 25.40816327 + t = 25.448292224 + 25.40816327 Combine like terms: -25.40816327 + 25.40816327 = 0.00000000 0.00000000 + t = 25.448292224 + 25.40816327 t = 25.448292224 + 25.40816327 Combine like terms: 25.448292224 + 25.40816327 = 50.856455494 t = 50.856455494 Simplifying t = 50.856455494Subproblem 2
t + -25.40816327 = -25.448292224 Simplifying t + -25.40816327 = -25.448292224 Reorder the terms: -25.40816327 + t = -25.448292224 Solving -25.40816327 + t = -25.448292224 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.40816327' to each side of the equation. -25.40816327 + 25.40816327 + t = -25.448292224 + 25.40816327 Combine like terms: -25.40816327 + 25.40816327 = 0.00000000 0.00000000 + t = -25.448292224 + 25.40816327 t = -25.448292224 + 25.40816327 Combine like terms: -25.448292224 + 25.40816327 = -0.040128954 t = -0.040128954 Simplifying t = -0.040128954Solution
The solution to the problem is based on the solutions from the subproblems. t = {50.856455494, -0.040128954}
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