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Simplifying 4.9t2 + 25t + -120 = 0 Reorder the terms: -120 + 25t + 4.9t2 = 0 Solving -120 + 25t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -24.48979592 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + 5.102040816t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + 5.102040816t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + 5.102040816t + t2 = 0 + 24.48979592 5.102040816t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 5.102040816t + t2 = 24.48979592 The t term is 5.102040816t. Take half its coefficient (2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. 5.102040816t + 6.507705122 + t2 = 24.48979592 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = 24.48979592 + 6.507705122 Combine like terms: 24.48979592 + 6.507705122 = 30.997501042 6.507705122 + 5.102040816t + t2 = 30.997501042 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 30.997501042 Calculate the square root of the right side: 5.567539945 Break this problem into two subproblems by setting (t + 2.551020408) equal to 5.567539945 and -5.567539945.Subproblem 1
t + 2.551020408 = 5.567539945 Simplifying t + 2.551020408 = 5.567539945 Reorder the terms: 2.551020408 + t = 5.567539945 Solving 2.551020408 + t = 5.567539945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = 5.567539945 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 5.567539945 + -2.551020408 t = 5.567539945 + -2.551020408 Combine like terms: 5.567539945 + -2.551020408 = 3.016519537 t = 3.016519537 Simplifying t = 3.016519537Subproblem 2
t + 2.551020408 = -5.567539945 Simplifying t + 2.551020408 = -5.567539945 Reorder the terms: 2.551020408 + t = -5.567539945 Solving 2.551020408 + t = -5.567539945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = -5.567539945 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -5.567539945 + -2.551020408 t = -5.567539945 + -2.551020408 Combine like terms: -5.567539945 + -2.551020408 = -8.118560353 t = -8.118560353 Simplifying t = -8.118560353Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.016519537, -8.118560353}
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