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Simplifying -5t2 + -5t + 40 = 0 Reorder the terms: 40 + -5t + -5t2 = 0 Solving 40 + -5t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -1t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + -1t + -1t2)' equal to zero and attempt to solve: Simplifying 8 + -1t + -1t2 = 0 Solving 8 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + t + t2 = 0 + 8 t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 t + t2 = 8 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 1.25 + t2 = 8.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (t + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
t + 0.5 = 2.872281323 Simplifying t + 0.5 = 2.872281323 Reorder the terms: 0.5 + t = 2.872281323 Solving 0.5 + t = 2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.872281323 + -0.5 t = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 t = 2.372281323 Simplifying t = 2.372281323Subproblem 2
t + 0.5 = -2.872281323 Simplifying t + 0.5 = -2.872281323 Reorder the terms: 0.5 + t = -2.872281323 Solving 0.5 + t = -2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.872281323 + -0.5 t = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 t = -3.372281323 Simplifying t = -3.372281323Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.372281323, -3.372281323}Solution
t = {2.372281323, -3.372281323}
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