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Simplifying -10t2 + 30t + 300 = 0 Reorder the terms: 300 + 30t + -10t2 = 0 Solving 300 + 30t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(30 + 3t + -1t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(30 + 3t + -1t2)' equal to zero and attempt to solve: Simplifying 30 + 3t + -1t2 = 0 Solving 30 + 3t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -3t + t2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -3t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -3t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -3t + t2 = 0 + 30 -3t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -3t + t2 = 30 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 30 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + -3t + t2 = 32.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (t + -1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
t + -1.5 = 5.678908346 Simplifying t + -1.5 = 5.678908346 Reorder the terms: -1.5 + t = 5.678908346 Solving -1.5 + t = 5.678908346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 5.678908346 + 1.5 t = 5.678908346 + 1.5 Combine like terms: 5.678908346 + 1.5 = 7.178908346 t = 7.178908346 Simplifying t = 7.178908346Subproblem 2
t + -1.5 = -5.678908346 Simplifying t + -1.5 = -5.678908346 Reorder the terms: -1.5 + t = -5.678908346 Solving -1.5 + t = -5.678908346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -5.678908346 + 1.5 t = -5.678908346 + 1.5 Combine like terms: -5.678908346 + 1.5 = -4.178908346 t = -4.178908346 Simplifying t = -4.178908346Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.178908346, -4.178908346}Solution
t = {7.178908346, -4.178908346}
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