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Simplifying -5t2 + -8t = -120 Reorder the terms: -8t + -5t2 = -120 Solving -8t + -5t2 = -120 Solving for variable 't'. Reorder the terms: 120 + -8t + -5t2 = -120 + 120 Combine like terms: -120 + 120 = 0 120 + -8t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -24 + 1.6t + t2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.6t + 24 + t2 = 0 + 24 Reorder the terms: -24 + 24 + 1.6t + t2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.6t + t2 = 0 + 24 1.6t + t2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.6t + t2 = 24 The t term is 1.6t. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6t + 0.64 + t2 = 24 + 0.64 Reorder the terms: 0.64 + 1.6t + t2 = 24 + 0.64 Combine like terms: 24 + 0.64 = 24.64 0.64 + 1.6t + t2 = 24.64 Factor a perfect square on the left side: (t + 0.8)(t + 0.8) = 24.64 Calculate the square root of the right side: 4.963869458 Break this problem into two subproblems by setting (t + 0.8) equal to 4.963869458 and -4.963869458.Subproblem 1
t + 0.8 = 4.963869458 Simplifying t + 0.8 = 4.963869458 Reorder the terms: 0.8 + t = 4.963869458 Solving 0.8 + t = 4.963869458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = 4.963869458 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = 4.963869458 + -0.8 t = 4.963869458 + -0.8 Combine like terms: 4.963869458 + -0.8 = 4.163869458 t = 4.163869458 Simplifying t = 4.163869458Subproblem 2
t + 0.8 = -4.963869458 Simplifying t + 0.8 = -4.963869458 Reorder the terms: 0.8 + t = -4.963869458 Solving 0.8 + t = -4.963869458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = -4.963869458 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = -4.963869458 + -0.8 t = -4.963869458 + -0.8 Combine like terms: -4.963869458 + -0.8 = -5.763869458 t = -5.763869458 Simplifying t = -5.763869458Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.163869458, -5.763869458}
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