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Simplifying 2t2 + -10t + -30 = 0 Reorder the terms: -30 + -10t + 2t2 = 0 Solving -30 + -10t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -5t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -5t + t2)' equal to zero and attempt to solve: Simplifying -15 + -5t + t2 = 0 Solving -15 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -5t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -5t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -5t + t2 = 0 + 15 -5t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -5t + t2 = 15 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 15 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 15 + 6.25 Combine like terms: 15 + 6.25 = 21.25 6.25 + -5t + t2 = 21.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (t + -2.5) equal to 4.609772229 and -4.609772229.Subproblem 1
t + -2.5 = 4.609772229 Simplifying t + -2.5 = 4.609772229 Reorder the terms: -2.5 + t = 4.609772229 Solving -2.5 + t = 4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 4.609772229 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 4.609772229 + 2.5 t = 4.609772229 + 2.5 Combine like terms: 4.609772229 + 2.5 = 7.109772229 t = 7.109772229 Simplifying t = 7.109772229Subproblem 2
t + -2.5 = -4.609772229 Simplifying t + -2.5 = -4.609772229 Reorder the terms: -2.5 + t = -4.609772229 Solving -2.5 + t = -4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -4.609772229 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -4.609772229 + 2.5 t = -4.609772229 + 2.5 Combine like terms: -4.609772229 + 2.5 = -2.109772229 t = -2.109772229 Simplifying t = -2.109772229Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.109772229, -2.109772229}Solution
t = {7.109772229, -2.109772229}
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