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Simplifying 2 + 4t + -10t2 = 0 Solving 2 + 4t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2t + -5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2t + -5t2)' equal to zero and attempt to solve: Simplifying 1 + 2t + -5t2 = 0 Solving 1 + 2t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -0.4t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4t + t2 = 0 + 0.2 -0.4t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4t + t2 = 0.2 The t term is -0.4t. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4t + 0.04 + t2 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4t + t2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4t + t2 = 0.24 Factor a perfect square on the left side: (t + -0.2)(t + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (t + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
t + -0.2 = 0.489897949 Simplifying t + -0.2 = 0.489897949 Reorder the terms: -0.2 + t = 0.489897949 Solving -0.2 + t = 0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = 0.489897949 + 0.2 t = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 t = 0.689897949 Simplifying t = 0.689897949Subproblem 2
t + -0.2 = -0.489897949 Simplifying t + -0.2 = -0.489897949 Reorder the terms: -0.2 + t = -0.489897949 Solving -0.2 + t = -0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = -0.489897949 + 0.2 t = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 t = -0.289897949 Simplifying t = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.689897949, -0.289897949}Solution
t = {0.689897949, -0.289897949}
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