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Simplifying -5t2 + 12t + 1 = 0 Reorder the terms: 1 + 12t + -5t2 = 0 Solving 1 + 12t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -2.4t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2.4t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2.4t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2.4t + t2 = 0 + 0.2 -2.4t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2.4t + t2 = 0.2 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = 0.2 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 0.2 + 1.44 Combine like terms: 0.2 + 1.44 = 1.64 1.44 + -2.4t + t2 = 1.64 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (t + -1.2) equal to 1.280624847 and -1.280624847.Subproblem 1
t + -1.2 = 1.280624847 Simplifying t + -1.2 = 1.280624847 Reorder the terms: -1.2 + t = 1.280624847 Solving -1.2 + t = 1.280624847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 1.280624847 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 1.280624847 + 1.2 t = 1.280624847 + 1.2 Combine like terms: 1.280624847 + 1.2 = 2.480624847 t = 2.480624847 Simplifying t = 2.480624847Subproblem 2
t + -1.2 = -1.280624847 Simplifying t + -1.2 = -1.280624847 Reorder the terms: -1.2 + t = -1.280624847 Solving -1.2 + t = -1.280624847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -1.280624847 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -1.280624847 + 1.2 t = -1.280624847 + 1.2 Combine like terms: -1.280624847 + 1.2 = -0.080624847 t = -0.080624847 Simplifying t = -0.080624847Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.480624847, -0.080624847}
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