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Simplifying 10t2 + -8t + -20 = 0 Reorder the terms: -20 + -8t + 10t2 = 0 Solving -20 + -8t + 10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -4t + 5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -4t + 5t2)' equal to zero and attempt to solve: Simplifying -10 + -4t + 5t2 = 0 Solving -10 + -4t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -0.8t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.8t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -0.8t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.8t + t2 = 0 + 2 -0.8t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.8t + t2 = 2 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 2 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 2 + 0.16 Combine like terms: 2 + 0.16 = 2.16 0.16 + -0.8t + t2 = 2.16 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (t + -0.4) equal to 1.469693846 and -1.469693846.Subproblem 1
t + -0.4 = 1.469693846 Simplifying t + -0.4 = 1.469693846 Reorder the terms: -0.4 + t = 1.469693846 Solving -0.4 + t = 1.469693846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 1.469693846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 1.469693846 + 0.4 t = 1.469693846 + 0.4 Combine like terms: 1.469693846 + 0.4 = 1.869693846 t = 1.869693846 Simplifying t = 1.869693846Subproblem 2
t + -0.4 = -1.469693846 Simplifying t + -0.4 = -1.469693846 Reorder the terms: -0.4 + t = -1.469693846 Solving -0.4 + t = -1.469693846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -1.469693846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -1.469693846 + 0.4 t = -1.469693846 + 0.4 Combine like terms: -1.469693846 + 0.4 = -1.069693846 t = -1.069693846 Simplifying t = -1.069693846Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.869693846, -1.069693846}Solution
t = {1.869693846, -1.069693846}
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