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Simplifying -16t2 + 4t + 3 = 0 Reorder the terms: 3 + 4t + -16t2 = 0 Solving 3 + 4t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + -0.25t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.25t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.25t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.25t + t2 = 0 + 0.1875 -0.25t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.25t + t2 = 0.1875 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 0.1875 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 0.1875 + 0.015625 Combine like terms: 0.1875 + 0.015625 = 0.203125 0.015625 + -0.25t + t2 = 0.203125 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (t + -0.125) equal to 0.450693909 and -0.450693909.Subproblem 1
t + -0.125 = 0.450693909 Simplifying t + -0.125 = 0.450693909 Reorder the terms: -0.125 + t = 0.450693909 Solving -0.125 + t = 0.450693909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 0.450693909 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 0.450693909 + 0.125 t = 0.450693909 + 0.125 Combine like terms: 0.450693909 + 0.125 = 0.575693909 t = 0.575693909 Simplifying t = 0.575693909Subproblem 2
t + -0.125 = -0.450693909 Simplifying t + -0.125 = -0.450693909 Reorder the terms: -0.125 + t = -0.450693909 Solving -0.125 + t = -0.450693909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -0.450693909 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -0.450693909 + 0.125 t = -0.450693909 + 0.125 Combine like terms: -0.450693909 + 0.125 = -0.325693909 t = -0.325693909 Simplifying t = -0.325693909Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.575693909, -0.325693909}
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