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Simplifying 5t2 + -1t = 3 Reorder the terms: -1t + 5t2 = 3 Solving -1t + 5t2 = 3 Solving for variable 't'. Reorder the terms: -3 + -1t + 5t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -1t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -0.2t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.2t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.2t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.2t + t2 = 0 + 0.6 -0.2t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.2t + t2 = 0.6 The t term is -0.2t. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2t + 0.01 + t2 = 0.6 + 0.01 Reorder the terms: 0.01 + -0.2t + t2 = 0.6 + 0.01 Combine like terms: 0.6 + 0.01 = 0.61 0.01 + -0.2t + t2 = 0.61 Factor a perfect square on the left side: (t + -0.1)(t + -0.1) = 0.61 Calculate the square root of the right side: 0.781024968 Break this problem into two subproblems by setting (t + -0.1) equal to 0.781024968 and -0.781024968.Subproblem 1
t + -0.1 = 0.781024968 Simplifying t + -0.1 = 0.781024968 Reorder the terms: -0.1 + t = 0.781024968 Solving -0.1 + t = 0.781024968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = 0.781024968 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = 0.781024968 + 0.1 t = 0.781024968 + 0.1 Combine like terms: 0.781024968 + 0.1 = 0.881024968 t = 0.881024968 Simplifying t = 0.881024968Subproblem 2
t + -0.1 = -0.781024968 Simplifying t + -0.1 = -0.781024968 Reorder the terms: -0.1 + t = -0.781024968 Solving -0.1 + t = -0.781024968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = -0.781024968 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = -0.781024968 + 0.1 t = -0.781024968 + 0.1 Combine like terms: -0.781024968 + 0.1 = -0.681024968 t = -0.681024968 Simplifying t = -0.681024968Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.881024968, -0.681024968}
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